1 

LIBRARY 

OF   THE 

Theological    Seminary, 

PRINCETON,    N.  J. 

i 
i 

Case, 

XILL 

Shelf, 

C-  re         , 

1 

Booh, 

i?.U 


♦^ 


POPULAE    LECTURES 


ON 


SCIENTIFIC    SUBJECTS. 


POPULAE    LECTUEES 


ON 


SCIENTIFIC    SUBJECTS. 


/  " 

H.  'hELMHOLTZ, 

PROFESSOR    OF    PHYSIC:J    IN    THE    UNIVEIISITX    OF    BERLIN. 


TEANSLATED  BY 

E.    ATKINSON,    Pu.D.    F.C.S. 

PBOPESSOR     OB-     EXPERIMENTAL     SCIENCE,     STAFF     COLLEGE. 


WITH      AN     INTRODUCTION 

BT 

.       PROFESSOR    TYNDALL. 


NEW  YOEK: 
D.    APPLETON    AND    COMPANY, 

549    &    551    BROADWAY. 
1873. 


AUTHOR'S   PREFACE, 


In  compliance  with  many  requests,  I  beg  to  offer  to 
the  public  a  series  of  popular  Lectures  which  I  have 
delivered  on  various  occasions.  They  are  designed  for 
readers  who,  without  being  professionally  occupied  with 
the  study  of  Natural  Science,  are  yet  interested  in  the 
scientific  results  of  such  studies.  The  difficulty,  felt  so 
strongly  in  printed  scientific  lectures,  namely,  that  the 
reader  cannot  see  the  experiments,  has  in  the  present 
case  been  materially  lessened  by  the  numerous  illustra- 
tions which  the  publishers  have  liberally  furnished. 

The  first  and  second  Lectures  have  already  appeared 
in  print;  the  first  in  a  university  programme  which, 
however,  was  not  published.  The  second  appeared  in 
the  'Kieler  Monatsschrift '  for  May,  1853,  but  owing  to 
the  restricted  circulation  of  that  journal,  became  but 
little  known  ;  both  have,  accordingly,  been  reprinted. 
The  third  and  fourth  Lectures  have  not  previously 
appeared. 

These  Lectures,  called  forth  as  they  have  been  by 
incidental  occasions,  have  not,  of  pourse,  been  composed 
in  accordance  y^iih.  a  rigidly  u.?\iforin  plan.  Each  of 
theii^  has  b^eiji  kep^  perfiectly  independent  of  the  others. 


viii  AUTHORS   PREFACE. 

Hence  some  amount  of  repetition  has  been  unavoidable, 
and  the  first  four  may  perhaps  seem  somewhat  confusedly 
thrown  together.  If  I  may  claim  that  they  have  any 
leading  thought,  it  would  be  that  I  have  endeavoured 
to  illustrate  the  essence  and  the  import  of  Natural 
laws,  and  their  relation  to  the  mental  activity  of  man. 
This  seems  to  me  the  chief  interest  and  the  chief  need 
in  Lectures  before  a  public  whose  education  has  been 
mainly  literary. 

I  have  but  little  to  remark  with  reference  to  individual 
Lectures.  The  set  of  Lectures,  which  treats  of  the  Theory 
of  Vision,  have  been  already  published  in  the  '  Preussische 
Jahrbiicher,'  and  have  acquired,  therefore,  more  of  the 
character  of  Eeview  articles.  As  it  was  possible  in 
this  second  reprint  to  render  many  points  clearer  by 
illustrations,  I  have  introduced  a  number  of  woodcuts, 
and  inserted  in  the  text  the  necessary  explanations.  A 
few  other  small  alterations  have  originated  in  my  having 
availed  myself  of  the  results  of  new  series  of  experiments. 
The  fifth  Lecture,  on  the  Interaction  of  Natural  Forces, 
originally  published  sixteen  years  ago,  could  not  be  left 
entirely  unaltered  in  this  reprint.  Yet  the  alterations 
have  been  as  slight  as  possible,  and  have  merely  been 
such  as  have  become  necessary  by  new  experimental 
facts,  which  partly  confirm  the  statements  originally 
made,  and  partly  modify  them. 

The  seventh  Lecture,  on  the  Conservation  of  Force, 
developes  still  further  a  portion  of  the  fifth.  Its  main 
object  is  to  elucidate  the  cardinal  physical  ideas  of  work, 
and  of  its  unalterability.  The  applications  and  con- 
sequences of  the  law  of  the  Conservation  of  Force  are 
comparatively  more  easy  to  grasp.    They  have  in  recent 


author's  preface.  ix 

times  been  treated  by  several  persons  in  a  vivid  and 
interesting  manner,  so  that  it  seemed  unnecessary  to 
publish  the  corresponding  part  of  the  cycle  of  lectures 
which  I  delivered  on  this  subject ;  the  more  so  as  some  of 
the  more  important  subjects  to  be  discussed  will,  perhaps 
in  the  immediate  future,  be  capable  of  more  definite 
treatment  than  is  at  present  possible. 

On  the  other  hand,  I  have  invariably  found  that  the 
fundamental  ideas  of  this  subject  always  appear  difficult 
of  comprehension  not  only  to  those  who  have  not  passed 
through  the  school  of  mathematical  mechanics ;  but  even 
to  those  who  attack  the  subject  with  diligence  and  in- 
telligence, and  who  possess  a  tolerable  acquaintance  with 
natural  science.  It  is  not  to  be  denied  that  these  ideas 
are  abstractions  of  a  quite  peculiar  kind.  Even  such  a 
mind  as  that  of  Kant  found  difficulty  in  comprehend- 
ing them  ;  as  is  shown  by  his  controversy  with  Leibnitz. 
Hence  1  thought  it  worth  while  to  furnish  in  a  popular  form 
an  explanation  of  these  ideas,  by  referring  them  to  many 
of  the  better  known  mechanical  and  physical  examples  ; 
and  therefore  I  have  only  for  the  present  given  the  first 
Lecture  of  that  series  which  is  devoted  to  this  object. 

The  last  Lecture  was  the  opening  address  for  the 
'  Naturforscher-Versammlung,'  in  Innsbriick.  It  was 
not  delivered  from  a  complete  manuscript,  but  from 
brief  notes,  and  was  not  written  out  until  a  year  after. 
The  present  form  has,  therefore,  no  claim  to  be  con- 
sidered an  accurate  reproduction  of  that  address.  I  have 
added  it  to  the  present  collection,  for  in  it  I  have  treated 
briefly  what  is  more  fully  discussed  in  the  other  articles. 
Its  title  to  the  place  which  it  occupies  lies  in  the  fact 
that   it   attempts  to  bring  the  views  enunciated  in  the 


X  author's  preface. 

preceding  Lectures  into  a  more  complete  and  more  com- 
prehensive whole. 

In  conclusion,  I  hope  that  these  Lectures  may  meet 
with  that  forbearance  which  lectures  always  require  when 
they  are  not  heard,  but  are  read  in  print. 

THE   AUTHOR. 


TEANSLATOR'S   PREFACE. 


In  bringing  this  Translation  of  Helmholtz's  Popular 
Scientific  Lectures  before  the  public,  I  have  to  thank 
Mr.  A.  J.  Ellis  for  having  placed  at  the  disposal  of  the 
Publishers  the  translation  of  the  third  Lecture ;  and  also 
Dr.  Francis,  the  Editor  of  the  '  Philosophical  Magazine,' 
for  giving  me  permission  to  use  the  translation  of  the 
fifth  Lecture,  which  originally  appeared  in  that  Journal. 
In  addition  to  the  Editorial  charge  of  the  book,  my 
own  task  has  been  limited  to  the  translation  of  two  of 
the  Lectures.  I  shoidd  have  hesitated  to  undertake  the 
work,  had  I  not  from  the  outset  been  able  to  rely  upon 
the  aid  of  several  gentlemen  whose  names  are  appended 
to  the  Contents.  One  advantage  gained  from  this  division 
of  labour  is,  that  the  publication  of  the  work  has  been 
accelerated  ;  but  a  far  more  important  benefit  has  been 
secured  to  it,  in  the  co-operation  of  translators  who  have 
brought  to  the  execution  of  their  task  special  knowledge 
of  their  respective  subjects. 

E.  ATKINSON. 

Staff  College: 
March  1873. 


CONTENTS. 


LECTTIRB  PAGE 

I.  On  the  Eelation  of  Natural  Science  to  Science  in 
General.  Translated  by  H.  W.  Eve,  Esq.,  M.A.,  F.C.S., 
Wellington  College 1 

II.  On  Goethe's  Scientific  Researches.     Translated  by  H.  W. 

Eve,  Esq 33 

III.  On  the    Physiological    Causes    of  Harmony    in    Music. 

Translated  by  A.  J.  Ellis,  Esq.,  M.A.,  F.R.S.        .         .         .61 

IV.  Ice   and   Glaciers.      Translated  by   Dr.   Atkinson,   F.C.S., 

Professor  of  Experimental  Science,  Staff  College    .         .         .107 

V.    On  the  Interaction   of   the   Natural  Forces.     Translated 

by  Professor  Tyndall,  LL.D.,  F.KS 153 

VI.  The  Recent  Progress  of  the  Theory  of  Vision.    Translated 

by  Dr.  Pye-Smith,  B.A.,  F.R.C.P.,  Guy's  Hospital : 

I.     The  Eye  as  an  Optical  Instrument        .         .         .         .197 

II.     The  Sensation  of  Sight 229 

m.     The  Perception  of  Sight 270 

VII.  On  the  Conservation  of  Force.    Translated  by  Dr.   At- 

kinson         .317 

VIU,    On  the  Aim  and  Progress  of  Physical  Science.     Translated 

by  Dr.  W.  Flight,  F.C.S.,  British  Museum   ,        .        .        .363 


INTRODUCTION. 


In  the  year  1850,  when  I  was  a  student  in  the  Univer- 
sity of  Marburg,  it  was  my  privilege  to  translate  for 
the  '  Philosophical  Magazine  '  the  celebrated  memoirs  of 
Clausius,  then  just  published,  on  the  Moving  Force  of 
Heat. 

In  1851,  through  the  liberal  courtesy  of  the  late  Pro- 
fessor Magnus,  I  was  enabled  to  pursue  my  scientific 
labours  in  his  laboratory  in  Berlin.  One  evening  during 
my  residence  there  my  friend  Dr.  Du  Bois-Kaymond  put 
a  pamphlet  into  my  hands,  remarking  that  it  was  '  the 
production  of  the  first  head  in  Europe  since  the  death  of 
Jacobi,'  and  that  it  ought  to  be  translated  into  English. 
Soon  after  my  return  to  England  I  translated  the  essay  and 
published  it  in  the  '  Scientific  Memoirs,'  then  brought  out 
under  the  joint-editorship  of  Huxley,  Henfrey,  Francis, 
and  myself. 

This  essay,  which  was  communicated  in  1847  to  the 
Physical  Society  of  Berlin,  has  become  sufficiently  famous 
since.  It  was  entitled  '  Die  Erhaltung  der  Kraft,'  and 
its  author  was  Helmholtz,  originally  Military  Physician 
in  the  Prussian  service,  afterwards  Professor  of  Physiology 
in  the  Universities  of  Konigsberg  and  Heidelberg,  and 
now  Professor  of  Physics  in  the  University  of  Berlin. 

Brought  thus  face  to  face  with  the  great  generalisation 
of  the  Conservation  of  Energy,  I  sought,  to  the  best  of 
my  ability,  to  master  it  by  independent  thought  in  all  its 
physical  details.     I  could  not  forget  my  indebtedness  to 


Xvi  INTRODUCTION. 

Helmholtz  and  Clausius,  or  fail  to  see  the  probable  in- 
flueuce  of  their  writiDgs  on  the  science  of  the  coming 
time.  For  many  years,  therefore,  it  was  my  habit  to 
place  every  physical  paper  published  by  these  eminent 
men  within  the  reach  of  purely  English  readers. 

The  translation  of  the  lecture  on  the  '  ^Yechselwirkung 
der  Naturkrafte,'  printed  in  the  following  series,  had  this 
ori<nn.  It  appears  here  with  the  latest  emendations  of 
the  author  introduced  by  Dr.  Atkinson. 

The  evident  aim  of  these  Lectures  is  to  give  to  those 
'  whose  education  has  been  mainly  literary,'  an  intelligent 
interest  in  the  researches  of  science.  Even  among  such 
persons  the  reputation  of  Helmholtz  is  so  great  as  to 
render  it  almost  superfluous  for  me  to  say  that  the  intel- 
lectual nutriment  here  offered  is  of  the  very  first  quality. 

Soon  after  the  publication  of  the  '  Tonempfindungen ' 
bv  Helmholtz,  I  endeavoured  to  interest  the  Messrs.  Long- 
man in  the  work,  urging  that  the  publication  of  a  trans- 
lation of  it  would  be  an  honour  to  their  house.  They 
went  carefully  into  the  question  of  expense,  took  sage 
counsel  regarding  the  probable  sale,  and  came  reluctantly 
to  the  conclusion  that  it  would  not  be  remunerative.^ 
I  then  recommended  the  translation  of  these  '  Populare 
Vortrage,'  and  to  this  the  eminent  publishers  immediately 
agreed. 

Hence  the  present  volume,  brought  out  under  the 
editorship  of  Dr.  Atkinson  of  the  Staff  College,  Sandhurst. 
The  names  of  the  translators  are,  I  think,  a  guarantee 
that  their  work  will  be  wortliy  of  their  original. 

JOHN  TYNDALL. 

Royal  Institution: 

MarLh  1873. 

'  Since  the  date  of  the  foregoing  letter  frim  Professor  Tyiidall,  Messrs. 
Longman  &  Co.  have  made  arrangements  for  the  translation  of  Helmholtz's 
Tonempfindungen,  by  Mr.  Alexander  J.  Ellis,  F.R.S.,  &c. 


ON  THE 

RELATION   OF  NATURAL  SCIENCE* 
TO   GENERAL   SCIENCE. 

ACADEMICAL   DISCOURSE   DELIVERED  AT  HEIDELBERG, 
NOVEMBER  22,  1862, 

Br  De.  H.  HELMHOLTZ,  sometime  peoeectob. 


To-day  we  are  met,  according  to  annual  custom,  in 
grateful  commemoration  of  an  enlightened  sovereign  of 
this  kingdom,  Charles  Frederick,  who,  in  an  age  when 
the  ancient  fabric  of  European  society  seemed  tottering 
to  its  fall,  strove,  with  lofty  purpose  and  untiring  zeal,  to 
promote  the  welfare  of  his  subjects,  and,  above  all,  their 
moral  and  intellectual  development.  Eightly  did  he 
judge  that  by  no  means  could  he  more  effectually  realise 
this  beneficent  intention  than  by  the  revival  and  the 
encouragement  of  this  University.  Speaking,  as  I  do,  on 
such  an  occasion,  at  once  in  the  name   and  in  the  pre- 

'  The  German  word  Naturwissenschaft  has  no  exact  equivalent  iu 
modern  English,  including,  as  it  does,  both  the  Physical  and  the  Natural 
Sciences.  Curioiisly  enough,  in  the  original  charter  of  the  Eoyal  Society, 
the  phrase  Natural  Knowledge  covers  the  same  ground,  but  is  there  used  in 
opposition  to  supernatural  knowledge.  (Note  in  Buckle's  Civilisation, 
vol.  ii.  p.  341.)— Tb. 


2  ON   THE   RELATION   OF 

sence  of  the  whole  University,  I  have  thought  it  well  to 
try  and  take,  as  far  as  is  permitted  by  the  narrow  stand- 
point of  a  single  student,  a  general  view  of  the  connection 
of  the  several  sciences,  and  of  their  study. 

It  may,  indeed,  be  thought  that,  at  the  present  day, 
those  relations  between  the  different  sciences  which  have 
led  us  to  combine  them  under  the  name  Univeraitas  Lit- 
terarum,  have  become  looser  than  ever.  We  see  scholars 
and  scientific  men  absorbed  in  specialities  of  such  vast 
extent,  that  the  most  universal  genius  cannot  hope  to 
master  more  than  a  small  section  of  our  present  range  of 
knowledge.  For  instance,  the  philologists  of  the  last 
three  centuries  found  ample  occupation  in  the  study  of 
Greek  and  Latin  ;  at  best  they  added  to  it  the  know- 
ledge of  two  or  three  European  languages,  acquired  for 
practical  purposes.  But  now  comparative  philology  aims 
at  nothing  less  than  an  acquaintance  with  all  the  lan- 
guages of  all  branches  of  the  human  family,  in  order 
to  deduce  from  them  the  laws  by  which  language  itself 
has  been  formed,  and  to  this  gigantic  task  it  has  already 
applied  itself  with  superhuman  industry.  Even  classical 
philology  is  no  longer  restricted  to  the  study  of  those 
works  which,  by  their  artistic  perfection  and  precision  of 
thought,  or  because  of  the  importance  of  their  contents, 
have  become  models  of  prose  and  poetry  to  all  ages.  On 
the  contrary,  we  have  learnt  that  eveiy  lost  fragment  of 
an  ancient  author,  every  gloss  of  a  pedantic  grammarian, 
eveiy  allusion  of  a  Byzantine  court-poet,  every  broken 
tombstone  found  in  the  wilds  of  Hungaiy  or  Spain  or 
Africa,  may  contribute  a  fresh  fact,  or  fresh  evidence,  and 
thus  serve  to  increase  our  knowledge  of  the  past.  And 
so  another  group  of  scholars  are  busy  with  the  vast 
scheme  of  collecting  and  cataloguing,  for  the  use  of  their 
successors,   every  available   relic   of  classical   antiquity. 


NATURAL   SCIENCE   TO    GENERAL   SCIENCE.  6 

Add  to  this,  in  history,  the  study  of  original  documents, 
the  critical  examination  of  parchments  and  papers  accumu- 
lated in  the  archives  of  states  and  of  towns  ;  the  combi- 
nation of  details  scattered  up  and  down  in  memoirs,  in 
correspondence,  and  in  biographies  ;  the  deciphering  of 
hieroglyphics  and  cuneiform  inscriptions  ;  in  natural 
history  the  more  and  more  comprehensive  classification 
of  minerals,  plants,  and  animals,  as  well  living  as  extinct ; 
and  there  opens  out  before  us  an  expanse  of  knowledge 
the  contemplation  of  which  may  well  bewilder  us.  In  all 
these  sciences  the  range  of  investigation  widens  as  fast  as 
the  means  of  observation  improve.  The  zoologists  of  past 
times  were  content  to  have  described  the  teeth,  the  hair, 
the  feet,  and  other  external  characteristics  of  an  animal. 
The  anatomist,  on  the  other  hand,  confined  himself  to 
human  anatomy,  so  far  as  he  could  make  it  out  by  the 
help  of  the  knife,  the  saw,  and  the  scalpel,  with  the 
occasional  aid  of  injections  of  the  vessels.  Human 
anatomy  then  passed  for  an  unusually  extensive  and  diffi- 
cult study.  Now  we  are  no  longer  satisfied  with  the 
comparatively  rpugh  science  which  bore  the  name  of 
human  anatomy,  and  which,  though  without  reason,  was 
thought  to  be  almost  exhausted.  We  have  added  to  it 
comparative  anatomy — that  is,  the  anatomy  of  all  animals 
—  and  microscopic  anatomy,  both  of  them  sciences  of 
infinitely  wider  range,  which  now  absorb  the  interest  of 
students. 

The  four  elements  of  the  ancients  and  of  mediaeval 
alchemy  have  been  increased  to  sixty-four,  the  last  four 
of  which  are  due  to  a  method  invented  in  our  own 
University,  which  promises  still  further  discoveries.^     But 

'  That  is  the  method  of  spectrum  analysis,  due  to  Bunsen  and  Kirchoff, 
both  of  Heidelberg.  The  elements  alluded  to  are  caesium  rubidium, 
tha!liu7n,  and  iridium. 


4  ON  THE   RELATION   OF 

not  merely  is  the  number  of  the  elements  far  greater,  the 
methods  of  producing  complicated  combinations  of  them 
have  been  so  vastly  improved,  that  what  is  called  organic 
chemistry,  which  embraces  only  compounds  of  carbon  with 
oxygen,  hydrogen,  nitrogen,  and  a  few  other  elements,  has 
already  taken  rank  as  an  independent  science. 

'  As  the  stars  of  heaven  for  multitude '  was  in  ancient 
times  the  natural  expression  for  a  number  beyond  our 
comprehension,  Pliny  even  thinks  it  almost  presumption 
('  rem  etiam  Deo  improbam ')  on  the  part  of  Hipparchus 
to  have  undertaken  to  count  the  stars  and  to  determine 
their  relative  positions.  And  yet  none  of  the  catalogues 
up  to  the  seventeenth  century,  constructed  without  the 
aid  of  telescopes,  give  more  than  from  1,000  to  1,500 
stars  of  magnitudes  from  the  first  to  the  fifth.  At  pre- 
sent several  observatories  are  eno^aged  in  continuino-  these 
catalogues  down  to  stars  of  the  tenth  magnitude.  So 
that  upwards  of  200,000  fixed  stars  are  to  be  catalogued 
and  their  places  accurately  determined.  The  immediate 
result  of  these  observations  has  been  the  discovery  of  a 
great  number  of  new  planets ;  so  that,  instead  of  the  six 
known  in  1781,  there  are  now  seventy-five.^ 

The  contemplation  of  tins  astounding  activity  in  all 
branches  of  science  may  well  make  us  stand  aghast  at 
the  audacity  of  man,  and  exclaim  with  the  Chorus  in  the 
'Antigone':  'Who  can  survey  the  whole  field  of  know- 
ledge ?  Who  can  grasp  the  clues,  and  then  thread  the 
labyrinth?'  One  obvious  consequence  of  this  vast  exten- 
sion of  the  limits  of  science  is,  that  every  student  is 
forced  to  choose  a  narrower  and  narrower  field  for  his  own 
studies,  and  can  only  keep  up  an  imperfect  acquaintance 
even  with  allied  fields  of  research.  It  almost  raises  a 
smile  to  hear  that  in  the  seventeenth  century  Kepler  was 

'  At  the  end  of  November  1864,  the  82nd  of  the  small  planets,  Alcmene, 
was  discovered.     There  are  now  109. 


XATUEAL   SCIEK-CE    TO   GET^RAL   SCIENCE.  5 

invited  to  Gratz  as  professor  of  mathematics  and  moral 
philosophy  ;  and  that  at  Leyden,  in  the  beginning  of  the 
eighteenth,  Boerhave  occupied  at  the  same  time  the  chairs 
of  botany,  chemistry,  and  clinical  medicine,  and  therefore 
practically  that  of  pharmacy  as  well.  At  present  we 
require  at  least  four  professors,  or,  in  an  university  with 
its  full  complement  of  teachers,  seven  or  eight,  to  repre- 
sent all  these  branches  of  science.  And  the  same  is  true 
of  other  faculties. 

One  of  my  strongest  motives  for  discussing  to-day  the 
connection  of  the  different  sciences  is  that  I  am  myself  a 
student  of  natural  philosophy  ;  and  that  it  has  been  made 
of  late  a  reproach  against  natural  philosophy  that  it  has 
struck  out  a  path  of  its  own,  and  has  separated  itself  more 
and  more  widely  from  the  other  sciences  which  are  united 
by  common  philological  and  historical  studies.  This  op- 
position has,  in  fact,  been  long  apparent,  and  seems  to  me 
to  have  grown  up  mainly  under  the  inSirence  of  the 
Hegelian  philosophy,  or,  at  any  rate,  to  Lave  been  brought 
out  into  more  distinct  relief  by  that  philosophy.  Cer- 
tainly, at  the  end  of  the  last  century,  when  the  Kantian 
philosophy  reigned  supreme,  such  a  schism  had  never 
been  proclaimed  ;  on  the  contrary,  Kant's  philosophy 
rested  on  exactly  the  same  ground  as  the  physical 
sciences,  as  is  evident  from  his  own  scientific  works,  es- 
pecially from  his  '  Cosmogony,'  based  upon  Newton's  Law 
of  Grravitation,  which  afterwards,  under  the  name  of 
Laplace's  Nebular  Hypothesis,  came  to  be  universally 
recognised.  The  sole  object  of  Kant*s  '  Critical  Phi- 
losophy '  was  to  test  the  sources  and  the  authority  of  our 
knowledge,  and  to  fix  a  definite  scope  and  standard  for 
the  researches  of  philosophy,  as  compared  with  other 
sciences.  According  to  his  teaching,  a  principle  disco- 
vered a  'priori  by  pure  thought  was  a  rule  applicable  to 
the  method  of  pure  thought,  and   nothing   further ;  it 


6  ox   THE   RELATION   OF 

could  contain  no  real,  positive  knowledge.  The  '  Phi- 
losophy of  Identity '  ^  was  bolder.  It  started  with  the 
hypothesis  that  not  only  spiritual  phenomena,  but  even 
the  actual  world — nature,  that  is,  and  man — were  the 
result  of  an  act  of  thought  on  the  part  of  a  creative 
mind,  similar,  it  was  supposed,  in  kind  to  the  human 
mind.  On  this  hypothesis  it  seemed  competent  for  the 
human  mind,  even  without  the  guidance  of  external  ex- 
perience, to  think  over  again  the  thoughts  of  the  Creator, 
and  to  rediscover  them  by  its  own  inner  activity.  Such 
was  the  view  with  which  the  '  Philosophy  of  Idertity '  set 
to  work  to  construct  a  priori  the  results  of  other  sciences. 
The  process  might  be  more  or  less  successful  in  matters  of 
theology,  law,  politics,  language,  art,  history,  in  short,  in 
all  sciences,  the  subject-matter  of  which  really  grows  out 
of  our  moral  nature,  and  which  are  therefore  properly 
classed  together  under  the  name  of  moral  sciences.  The 
state,  the  church,  art,  and  language,  exist  in  order  to 
satisfy  certain  moral  needs  of  man.  Accordingly,  what- 
ever obstacles  nature,  or  chance,  or  the  rivalry  of  other 
men  may  interpose,  the  efforts  of  the  human  mind  to 
satisfy  its  needs,  being  systematically  directed  to  one 
end,  must  eventually  triumph  over  all  such  fortuitous 
hindrances.  Under  these  circumstances,  it  would  not  be 
a  downright  impossibility  for  a  philosopher,  starting  from 
an  exact  knowledge  of  the  mind,  to  predict  the  general 
course  of  human  development  under  the  above-named 
conditions,  especially  if  he  has  before  his  eyes  a  basis  of 
observed  facts,  on  which  to  build  his  abstractions.  More- 
over, Hegel  was  materially  assisted,  in  his  attempt  to 
solve  this  problem,  by  the  profound  and  philosophical 
views  on  historical  and  scientific  subjects,  with  which  the 
writings  of  his  immediate  predecessors,  both  poets  and 

'  So  called  because  it  proclaimed  the  identity  not  only  of  subject  and 
object,  but  of  contradictories,  such  as  existence  and  non-existence. — Te. 


NATUEAL    SCIENCE    TO    GENERAL    SCIENCE.  t 

philosophers,  abound.  He  had,  for  the  most  part,  only  to 
collect  and  combine  them,  in  order  to  produce  a  system 
calculated  to  impress  people  by  a  number  of  acute  and 
original  observations.  He  thus  succeeded  in  gaining  the 
enthusiastic  approval  of  most  of  the  educated  men  of  his 
time,  and  in  raising  extravagantly  sanguine  hopes  of 
solving  the  deepest  enigma  of  human  life  ;  all  the  more 
sanguine  doubtless,  as  the  connection  of  his  system  was 
disguised  under  a  strangely  abstract  phraseology,  and  was 
perhaps  really  understood  by  but  few  of  his  worshippers. 

But  even  granting  that  Hegel  was  more  or  less  suc- 
cessful in  constructing,  a  priori,  the  leading  results  of 
the  moral  sciences,  still  it  was  no  proof  of  the  correctness 
of  the  hypothesis  of  Identity,  with  which  he  started. 
The  facts  of  nature  would  have  been  the  crucial  test. 
That  in  the  moral  sciences  traces  of  the  activity  of  the 
human  intellect  and  of  the  several  stages  of  its  develop- 
ment should  present  themselves,  was  a  matter  of  course ; 
but  surely,  if  nature  really  reflected  the  result  of  the 
thought  of  a  creative  mind,  the  system  ought,  without 
difficulty,  to  find  a  place  for  her  comparatively  simple 
phenomena  and  processes.  It  was  at  this  point  that 
Hegel's  philosophy,  we  venture  to  say,  utterly  broke 
down.  His  system  of  nature  seemed,  at  least  to  natural 
philosophers,  absolutely  crazy.  Of  all  the  distinguished 
scientific  men  who  were  his  contemporaries,  not  one  was 
found  to  stand  up  for  his  ideas.  Accordingly,  Hegel 
himself,  convinced  of  the  importance  of  winning  for 
his  philosophy  in  the  field  of  physical  science  that  recog- 
nition which  had  been  so  freely  accorded  to  it  elsewhere, 
launched  out,  with  unusual  vehemence  and  acrimony, 
against  the  natural  philosophers,  and  especially  against 
Sir  Isaac  Newton,  as  the  first  and  greatest  representative 
of  physical  investigation.  The  philosophers  accused  the 
scientific  men  of  narrowness ;  the  scientific  men  retorted 


8  ON   THE   RELATION   OF 

that  the  philosophers  were  crazy.  And  so  it  came  aboiif. 
that  men  of  science  began  to  lay  some  stress  on  the 
banishment  of  all  philosophic  influences  from  their  work ; 
while  some  of  them,  including  men  of  the  greatest  acute- 
ness,  went  so  far  as  to  condemn  philosophy  altogether, 
not  merely  as  useless,  but  as  mischievous  dreaming. 
Thus,  it  must  be  confessed,  not  only  were  the  illegitimate 
pretensions  of  the  Hegelian  system  to  subordinate  to 
itself  all  other  studies  rejected,  but  no  regard  was  paid 
to  the  rightful  claims  of  philosophy,  that  is,  the  criticism 
of  the  sources  of  cognition,  and  the  definition  of  the 
functions  of  the  intellect. 

In  the  moral  sciences  the  course  of  things  was  dif- 
ferent, though  it  ultimately  led  to  almost  the  same 
result.  In  all  branches  of  those  studies,  in  theology, 
politics,  jurisprudence,  aesthetics,  philology,  there  started 
up  enthusiastic  Hegelians,  who  tried  to  reform  their 
several  departments  in  accordance  with  the  doctrines  of 
their  master,  and,  by  the  royal  road  of  speculation,  to 
reach  at  once  the  promised  land  and  gather  in  the 
harvest,  which  had  hitherto  only  been  approached  by 
long  and  laborious  study.  And  so,  for  some  time,  a  hard 
and  fast  line  was  drawn  between  the  moral  and  the 
physical  sciences  ;  in  fact,  the  very  name  of  science  was 
often  denied  to  the  latter. 

The  feud  did  not  long  subsist  in  its  original  intensity. 
The  physical  sciences  proved  conspicuously,  by  a  brilliant 
series  of  discoveries  and  practical  applications,  that  they 
contained  a  liealthy  germ  of  extraordinary  fertility ;  it 
was  impossible  any  longer  to  withhold  from  them  recog- 
nition and  respect.  And  even  in  other  departments  of 
science,  conscientious  investigators  of  facts  soon  pro- 
tested j^ gainst  the  over-bold  flights  of  speculation.  Still, 
it  cannot  be  overlooked  that  the  philosophy  of  Hegel  and 
Schelling  did  exercise  a  beneficial  influence ;  since  their 


NATURAL    SCIENCE   TO    GENERAL   SCIENCE.  9 

time  the  attention  of  investigators  in  the  moral  sciences 
had  been  constantly  and  more  keenly  directed  to  the 
scope  of  those  sciences,  and  to  their  intellectual  con- 
tents, and  therefore  the  great  amount  of  labour  bestowed 
on  those  systems  has  not  been  entirely  thrown  away. 

We  see,  then,  that  in  proportion  as  the  experimental 
investigation  of  facts  has  recovered  its  importance  in  the 
moral  sciences,  the  opposition  between  them  and  the 
physical  sciences  has  become  less  and  less  marked.  Yet 
we  must  not  forget  that,  though  this  opposition  was 
brought  out  in  an  unnecessarily  exaggerated  form  by  the 
Hegelian  philosophy,  it  has  its  foundation  in  the  nature 
of  things,  and  must,  sooner  or  later,  make  itself  felt.  It 
depends  partly  on  the  nature  of  the  intellectual  processes 
the  two  groups  of  sciences  involve,  partly,  as  their  very 
names  imply,  on  the  subjects  of  which  they  treat.  It  is 
not  easy  for  a  scientific  man  to  convey  to  a  scholar  or  a 
jurist  a  clear  idea  of  a  complicated  process  of  nature  ; 
he  must  demand  of  them  a  certain  power  of  abstraction 
from  the  phenomena,  as  well  as  a  certain  skill  in  the  use 
of  geometrical  and  mechanical  conceptions,  in  which  it  is 
difficult  for  them  to  follow  him.  On  the  other  liand  an 
artist  or  a  theologian  will  perhaps  find  the  natural  philo- 
sopher too  much  inclined  to  mechanical  and  material 
explanations,  which  seem  to  them  commonplace,  and 
chilling  to  their  feeling  and  enthusiasm.  Nor  will  the 
scholar  or  the  historian,  who  have  some  common  ground 
with  the  theologian  and  the  jurist,  fare  better  with  the 
natural  philosopher.  They  will  find  him  shockingly 
indifferent  to  literary  treasures,  perhaps  even  more  in- 
different than  he  ought  to  be  to  the  history  of  his  own 
science.  In  short,  there  is  no  denying  that,  while  the 
moral  sciences  deal  directly  with  the  nearest  and  dearest 
interests  of  the  human  mind,  and  with  the  institutions 
it  has  brought  into  being,  the  natural  sciences  are  con- 


10  ox   THE   RELATION   OF 

cerned  with  dead,  iDdifferent  matter,  obviously  indispen- 
sable for  the  sake  of  its  practical  utility,  but  apparently 
without  any  immediate  bearing  on  the  cultivation  of  the 
intellect. 

It  has  been  shown,  then,  that  the  sciences  have 
branclied  out  into  countless  ramifications,  that  there  has 
grown  up  between  different  groups  of  them  a  real  and 
deeply-felt  opposition,  tliat  finally  no  single  intellect  can 
embrace  the  whole  range,  or  even  a  considerable  por- 
tion of  it.  Is  it  still  reasonable  to  keep  them  together 
in  one  place  of  education?  Is  the  union  of  the  four 
Faculties  to  form  one  University  a  mere  relic  of  the 
Middle  Ages  ?  Many  valid  arguments  have  been  adduced 
for  separating  them.  Why  not  dismiss  the  medical 
faculty  to  the  hospitals  of  our  great  towns,  the  scientific 
men  to  the  Polytechnic  Schools,  and  form  special  semin- 
aries for  the  theologians  and  jurists?  Long  may  the 
Grerman  universities  be  preserved  from  such  a  fate ! 
Then,  indeed,  would  the  connection  between  the  dif- 
ferent sciences  be  finally  broken.  How  essential  that 
connection  is,  not  only  from  an  university  point  of  view, 
as  tending  to  keep  alive  the  intellectual  energy  of  the 
country,  but  also  on  material  grounds,  to  secure  the 
successful  application  of  that  energy,  will  be  evident 
from  a  few  considerations. 

First,  then,  I  would  say  that  union  of  the  different 
P'aculties  is  necessary  to  maintain  a  healthy  equilibrium 
among  the  intellectual  energies  of  students.  Each  study 
tries  certain  of  our  intellectual  faculties  more  than  the 
rest,  and  strengthens  them  accordingly  by  constant  exer- 
cise. But  any  sort  of  one-sided  development  is  attended 
with  danger ;  it  disqualifies  us  for  using  those  faculties 
that  are  less  exercised,  and  so  renders  us  less  capable  of 
a  general  view  ;  above  all  it  leads  us  to  overvalue  our- 
selves.    Anyone  who  has  found  himself  much  more  sue- 


NATURAL   SCIENCE   TO   GENERAL   SCIENCE.  11 

cessful  than  others  in  some  one  department  of  intellectual 
labour,  is  apt  to  forget  that  there  are  many  other  things 
which  they  can  do  better  than  he  can :  a  mistake — I 
would  have  every  student  remember — which  is  the  worst 
enemy  of  all  intellectual  activity. 

How  many  men  of  ability  have  forgotten  to  practise 
that  criticism  of  themselves  which  is  so  essential  to  the 
student,  and  so  hard  to  exercise,  or  have  been  completely 
crippled  in  their  progress,  because  they  have  thought 
dry,  laborious  drudgery  beneath  them,  and  have  devoted 
all  their  energies  to  the  quest  of  brilliant  theories  and 
wonder-working  discoveries  !  How  many  such  men  have 
become  bitter  misanthropes,  and  put  an  end  to  a  melan- 
choly existence,  because  they  have  failed  to  obtain  among 
their  fellows  that  recognition  which  must  be  won  by 
labour  and  results,  but  which  is  ever  withheld  from 
mere  self-conscious  genius  !  And  the  more  isolated  a 
man  is,  the  more  liable  is  he  to  this  danger ;  while, 
on  the  other  hand,  nothing  is  more  inspiriting  than  to 
feel  yourself  forced  to  strain  every  nerve  to  win  the 
admiration  of  men  whom  you,  in  your  turn,  must 
admire. 

In  comparing  the  intellectual  processes  involved  in  the 
pursuit  of  the  several  branches  of  science,  we  are  struck  by 
certain  generic  differences,  dividing  one  group  of  sciences 
from  another.  At  the  same  time  it  must  not  be  forgotten 
that  every  man  of  conspicuous  ability  has  his  own  special 
mental  constitution,  which  fits  him  for  one  line  of 
thought  rather  than  another.  Compare  the  work  of 
two  contemporary  investigators  even  in  closely-allied 
branches  of  science,  and  you  will  generally  be  able  to 
convince  yourself  that  the  more  distinguished  the  men 
are,  the  more  clearly  does  their  individuality  come  out, 
and  the  less  qualified  woujd  either  of  them  be  to  carry 
on  the  other's  researphes,  To-day  I  can,  of  course,  do 
"2 


12  ON  THE   RELATION   OF 

nothing  more  than  characterise  some  of  the  most  general 
of  these  differences. 

I  have  ah-eacly  noticed  the  enormous  mass  of  the 
materials  accumulated  by  science.  It  is  obvious  that 
the  organisation  and  arrangement  of  them  must  be  pro- 
portionately perfect,  if  we  are  not  to  be  hopelessly  lost  in 
the  maze  of  erudition.  One  of  the  reasons  why  we  can 
so  far  surpass  our  predecessors  in  each  individual  study 
is  that  they  have  shown  us  how  to  organise  our  know- 
ledge. 

This  organisation  consists,  in  the  first  place,  of  a 
mechanical  arrangement  of  materials,  such  as  is  to  be 
found  in  our  catalogues,  lexicons,  registers,  indexes, 
digests,  scientific  and  literary  annuals,  systems  of  natural 
history,  and  the  like.  By  these  appliances  thus  much 
at  least  is  gained,  that  such  knowledge  as  cannot  be 
carried  about  in  the  memory  is  immediately  accessible  to 
anyone  who  wants  it.  With  a  good  lexicon  a  school-boy 
of  the  present  day  can  achieve  results  in  the  interpreta- 
tion of  the  classics,  which  an  Erasmus,  with  the  erudition 
of  a  lifetime,  could  hardly  attain.  Works  of  this  kind 
form,  so  to  speak,  our  intellectual  principal,  with  the 
interest  of  which  we  trade ;  it  is,  so  to  speak,  like 
capital  invested  in  land.  The  learning  buried  in  cata- 
logues, lexicons,  and  indexes  looks  as  bare  and  uninviting 
as  the  soil  of  a  farm ;  the  uninitiated  cannot  see  or  ap- 
preciate the  labour  and  capital  already  invested  there  ; 
to  them  the  work  of  the  ploughman  seems  infinitely 
dull,  weary,  and  monotonous.  But  though  the  compiler 
of  a  lexicon  or  of  a  system  of  natural  history  must  be 
prepared  to  encounter  labour  as  weary  and  as  obstinate 
as  the  ploughman's,  yet  it  need  not  be  supposed  that  his 
work  is  of  a  low  type,  or  that  it  is  by  any  means  as  dry 
and  mechanical  as  it  looks  when  we  have  it  before  us  in 
black  and  white.     In  this,  as  in  any  other  sort  of  scien- 


NATURAL   SCIENCE   TO   GENERAL   SCIENCE.  13 

tific  work,  it  is  necessary  to  discover  every  fact  by 
careful  observation,  then  to  verify  and  collate  them,  and 
to  separate  what  is  important  from  what  is  not.  All 
this  requires  a  man  with  a  thorough  grasp,  both  of  the 
object  of  the  compilation,  and  of  the  matter  and  methods 
of  the  science ;  and  for  such  a  man  every  detail  has  its 
bearing  on  the  whole,  and  its  special  interest.  Otherwise 
dictionary-making  would  be  the  vilest  drudgery  imagin- 
able.^ That  the  influence  of  the  progressive  development 
of  scientific  ideas  extends  to  these  works  is  obvious  from 
the  constant  demand  for  new  lexicons,  new  natural 
histories,  new  digests,  new  catalogues  of  stars,  all  denot- 
ing advancement  in  the  art  of  methodising  and  organis- 
ing science. 

But  our  knowledge  is  not  to  lie  dormant  in  the  shape 
of  catalogues.  The  very  fact  that  we  must  carry  it  about 
in  black  and  white  shows  that  our  intellectual  mastery  of 
it  is  incomplete.  It  is  not  enough  to  be  acquainted  with 
the  facts;  scientific  knowledge  begins  only  when  their 
laws  and  their  causes  are  unveiled.  Our  materials  must 
be  worked  up  by  a  logical  process  ;  and  the  first  step  is  to 
connect  like  with  like,  and  to  elaborate  a  general  concep- 
tion embracing  them  all.  Such  a  conception,  as  the 
name  implies,  takes  a  number  of  single  facts  together, 
and  stands  as  their  representative  in  our  mind.  We  call 
it  a  general  conception,  or  the  conception  of  a  genus, 
when  it  embraces  a  number  of  existing  objects ;  we  call  it 
a  law  when  it  embraces  a  series  of  incidents  or  occurrences. 
When,  for  example,  I  have  made  out  that  all  mammals — 
that  is,  all  warm-blooded,  viviparous  animals — breathe 
through  lungs,  have  two  chambers  in  the  heart  and  at 
least  three  tympanal  bonef?,  I  need  no  longer  remember 
these  anatomical  peculiarities  in  the  individual  cases  of 
the  monkey,  the  dog,  the  horse,  and  the  whale ;  the 
*  Condendaque  lexica  mandat  damnatis. — Tb. 


14  ON   THE   RELATION   OF  1 

general  rule  includes  a  vast  number  of  single  instances, 
and  represents  them  in  my  memory.  When  I  enunciate 
the  law  of  refraction,  not  only  does  this  law  embrace  all 
cases  of  rays  falling  at  all  possible  angles  on  a  plane  sur- 
face of  water,  and  inform  me  of  the  residt,  but  it  includes 
all  cases  of  rays  of  any  colour  incident  on  transparent 
surfaces  of  any  form  and  any  constitution  whatsoever. 
This  law,  therefore,  includes  an  infinite  number  of  cases, 
which  it  would  have  been  absolutely  impossible  to  carry 
in  one's  memory.  Moreover,  it  should  be  noticed  that 
not  only  does  this  law  include  the  cases  which  we  our- 
selves or  other  men  have  already  observed,  but  that  we 
shall  not  hesitate  to  apply  it  to  new  cases,  not  yet  ob- 
served, with  absolute  confidence  in  the  reliability  of  our 
results.  In  the  same  way,  if  we  were  to  find  a  new  species 
of  mammal,  not  yet  dissected,  we  are  entitled  to  assume, 
with  a  confidence  bordering  on  a  certainty,  that  it  has 
lungs,  two  chambers  in  the  heart,  and  three  or  more 
tympanal  bones. 

Thus,  when  we  combine  the  results  of  experience  by  a 
process  of  thought,  and  form  conceptions,  whether  general 
conceptions  or  laws,  we  not  only  bring  our  knowledge 
into  a  form  in  which  it  can  be  easily  used  and  easily  re- 
tained, but  we  actually  enlarge  it,  inasmuch  as  we  feel 
ourselves  entitled  to  extend  the  rules  and  the  laws  we 
have  discovered  to  all  similar  cases  that  may  be  hereafter 
presented  to  us. 

Tlie  above-mentioned  examples  are  of  a  class  in  which 
the  mental  process  of  combining  a  number  of  single  cases 
so  as  to  form  conceptions  is  unattended  by  farther  diffi- 
culties, and  can  be  distinctly  followed  in  all  its  stages. 
But  in  complicated  cases  it  is  not  so  easy  completely  to 
separate  like  facts  from  unlike,  and  to  combine  them  into 
a  clear,  well-defined  conception.  Assume  that  we  know  a 
man  to  be  ambitious ;  we  shall  perhaps  be  able  to  predict 


NATURAL   SCIENCE   TO   GENERAL   SCIENCE.  15 

with  tolerable  certainty  that  if  he  has  to  act  under  certain 
conditions,  he  will  follow  the  dictates  of  his  ambition, 
and  decide  on  a  certain  line  of  action.  But,  in  the  first 
place,  we  cannot  define  with  absolute  precision  what  con- 
stitutes an  ambitious  man,  or  by  what  standard  the  inten- 
sity of  his  ambition  is  to  be  measured  ;  nor,  again,  can  we 
say  precisely  what  degree  of  ambition  must  operate  in 
order  to  impress  the  given  direction  on  the  actions  of  the 
man  under  those  particular  circumstances.  Accordingly, 
we  institute  comparisons  between  the  actions  of  the  man 
in  question,  as  far  as  we  have  hitherto  observed  them,  and 
those  of  other  men  who  in  similar  cases  have  acted  as  he 
has  done,  and  we  draw  our  inference  respecting  his  future 
actions  without  being  able  to  express  either  the  major  or 
the  minor  premiss  in  a  clear,  sharply-defined  form — 
perhaps  even  without  having  convinced  ourselves  that  our 
anticipation  rests  on  such  an  analogy  as  I  have  described. 
In  such  cases  our  decision  proceeds  only  from  a  certain 
psychological  instinct,  not  from  conscious  reasoning, 
though  in  reality  we  have  gone  through  an  intellectual 
process  identical  with  that  which  leads  us  to  assume  that 
a  newly-discovered  mammal  has  lungs. 

This  latter  kind  of  induction,  which  can  never  be  per- 
fectly assimilated  to  forms  of  'logical  reasoning,  nor 
pressed  so  far  as  to  establish  universal  laws,  plays  a  most 
important  part  in  human  life.  The  whole  of  the  process 
by  which  we  translate  our  sensations  into  perceptions 
depends  upon  it,  as  appears  especially  from  the  investiga- 
tion of  what  are  called  illusions.  For  instance,  when  the 
retina  of  the  eye  is  irritated  by  a  blow,  we  imagine  we 
see  a  light  in  our  field  of  vision,  because  we  have, 
throughout  our  lives,  felt  irritation  in  the  optic  nerves 
only  when  there  was  light  in  the  field  of  vision,  and  have 
become  accustomed  to  identify  the  sensations  of  those 
nerves  with  the  presence  of  light  in  the  field  of  vision. 


16  ON  THE   RELATION   OF 

Moreover,  such  is  the  complexity  of  the  influences  affect- 
ing the  formation  both  of  character  in  general  and  of  the 
mental  condition  at  any  given  moment,  that  this  same 
kind  of  induction  necessarily  plays  a  leading  part  in  the 
investigation  of  psychological  processes.  In  fact,  in 
ascribing  to  ourselves  free-will,  that  is,  full  power  to  act 
as  we  please,  without  being  subject  to  a  stern  inevitable 
law  of  causality,  we  deny  in  toto  the  possibility  of  re- 
ferring at  least  one  of  the  ways  in  which  our  mental 
activity  expresses  itself  to  a  rigorous  law. 

We  might  possibly,  in  opposition  to  logical  induction 
which  reduces  a  question  to  clearly-defined  universal 
propositions,  call  this  kind  of  reasoning  cesthetic  induc- 
tion, because  it  is  most  conspicuous  in  the  higher  class  of 
works  of  art.  It  is  an  essential  part  of  an  artist's  talent 
to  reproduce  by  words,  by  form,  by  colour,  or  by  music, 
tlie  external  indications  of  a  character  or  a  state  of  mind, 
and  by  a  kind  of  instinctive  intuition,  uncontrolled  by 
any  definable  rule,  to  seize  the  necessary  steps  by  which 
we  pass  from  one  mood  to  another.  If  we  do  find  that 
the  artist  has  consciously  worked  after  general  rules  and 
abstractions,  we  think  his  work  poor  and  commonplace, 
and  cease  to  admire.  On  the  contrary,  the  works  of 
great  artists  bring  before  us  characters  and  moods  with 
such  a  lifelikeness,  with  such  a  wealth  of  individual  traits 
and  such  an  overwhelming  conviction  of  truth,  that  they 
almost  seem  to  be  more  real  than  the  reality  itself,  because 
all  disturbing  influences  are  eliminated. 

Now  if,  after  these  reflections,  we  proceed  to  review 
the  different  sciences,  and  to  classify  them  according  to 
the  method  by  which  they  must  arrive  at  their  results, 
we  are  brought  face  to  face  with  a  generic  difference 
between  the  natural  and  the  moral  sciences.  The  natural 
sciences  are  for  the  most  part  in  a  position  to  reduce  their 
inductions  to  sharply-defined  general  rules  and  principles ; 


NATURAL   SCIENCE   TO   GENERAL   SCIENCE.  17 

the  moral  sciences,  on  the  other  hand,  have,  in  by  far  the 
most  numerous  cases,  to  do  with  conclusions  arrived  at  by 
psychological  instinct.  Philology,  in  so  far  as  it  is  con- 
cerned with  the  interpretation  and  emendation  of  the 
texts  handed  down  to  us,  must  seek  to  feel  out,  as  it  were, 
the  meaning  which  the  author  intended  to  express,  and 
the  accessory  notions  which  he  wished  his  words  to 
suggest ;  and  for  that  purpose  it  is  necessary  to  start  with 
a  correct  insight,  both  into  the  personality  of  the  author, 
and  into  the  genius  of  the  language  in  which  he  wrote. 
All  this  affords  scope  for  aesthetic,  but  not  for  strictly 
logical  induction.  It  is  only  possible  to  pass  judgment, 
if  you  have  ready  in  your  memory  a  great  number  of 
similar  facts,  to  be  instantaneously  confronted  with  the 
question  you  are  trying  to  solve.  Accordingly,  one  of 
the  first  requisites  for  studies  of  this  class  is  an  accurate 
and  ready  memory.  Many  celebrated  historians  and 
philologists  have,  in  fact,  astounded  their  contemporaries 
by  their  extraordinary  strength  of  memory.  Of  coai*se 
memory  alone  is  insufficient  without  a  knack  of  every- 
where discovering  real  resemblance,  and  without  a  deli- 
cately and  fully  trained  insight  into  the  springs  of  human 
action ;  while  this  again  is  unattainable  without  a  certain 
warmth  of  sympathy  and  an  interest  in  observing  the 
working  of  other  men's  minds.  Intercourse  with  our 
fellow-men  in  daily  life  must  lay  the  foundation  of  this 
insight,  but  the  study  of  history  and  art  serves  to  make 
it  richer  and  completer,  for  there  we  see  men  acting 
under  comparatively  unusual  conditions,  and  thus  come 
to  appreciate  the  full  scope  of  the  energies  which  lie 
hidden  in  our  breasts. 

None  of  this  group  of  sciences,  except  grammar,  lead 
us,  as  a  rule,  to  frame  and  enunciate  general  laws,  valid 
under  all  circumstances.  The  laws  of  grammar  are  a 
product  of  the  human  will,  though  they  can  hardly  be 


18  ON  THE  KELATION   OF 

said  to  have  been  framed  deliberately,  but  rather  to  have 
grown  up  gradually,  as  they  were  wanted.  Accordingly, 
they  present  themselves  to  a  learner  rather  in  the  form 
cf  commands,  that  is,  of  laws  imposed  by  external  au- 
thority. 

With  these  sciences  theology  and  jurisprudence  are 
naturally  connected.  In  fact,  certain  branches  of  history 
and  philology  serve  both  as  stepping-stones  and  as  hand- 
maids to  them.  The  general  laws  of  theology  and  juris- 
prudence are  likewise  commands,  laws  imposed  by  external 
authority  to  regulate,  from  a  moral  or  juridical  point  of 
view,  the  actions  of  mankind  ;  not  laws  which,  like  those 
of  natm*e,  contain  generalisations  from  a  vast  multitude 
of  facts.  At  the  same  time  the  application  of  a  gramma- 
tical, legal,  moral,  or  theological  rule  is  couched,  like  the 
application  of  a  law  of  nature  to  a  particular  case,  in  the 
forms  of  logical  inference.  The  rule  forms  the  major 
premiss  of  the  syllogism,  while  the  minor  must  settle 
whether  the  case  in  question  satisfies  the  conditions  to 
which  the  rule  is  intended  to  apply.  The  solution  of  this 
latter  problem,  whether  in  grammatical  analysis,  where 
the  meaning  of  a  sentence  is  to  be  evolved,  or  in  the  legal 
criticism  of  the  credibility  of  the  facts  alleged,  of  the 
intentions  of  the  parties,  or  of  the  meaning  of  the  docu- 
ments they  have  put  into  court,  will,  in  most  cases,  be 
again  a  matter  of  psychological  insight.  On  the  other 
hand,  it  should  not  be  forgotten  that  both  the  syntax  of 
full3^-developed  languages  and  a  system  of  jurisprudence 
gradually  elaborated,  as  ours  has  been,  by  the  practice  of 
more  than  2,000  years,^  have  reached  a  high  pitch  of 
logical  completeness  and  consistency  ;  so  that,  speaking 
generally,  the  cases  which  do  not  obviously  fall  under 

'  It  should  be  remembered  that  the  Eoman  law,  uhich  has  only  parti- 
ally and  indirectly  influenced  English  practice,  is  tliw  recognised  basis  of 
Geiinan  jurisprudence. — Tb. 


NATURAL   SCIENCE   TO   GENERAL   SCIENCE.  19 

some  one  or  other  of  the  laws  actually  laid  down  are 
quite  exceptional.  Such  exceptions  there  will  always  be, 
for  the  legislation  of  man  can  never  have  the  absolute 
consistency  and  perfection  of  the  laws  of  nature.  In 
such  cases  there  is  no  course  open  but  to  try  and  guess 
the  intention  of  the  legislator  ;  or,  if  needs  be,  to 
supplement  it  after  the  analogy  of  his  decisions  in 
similar  cases. 

Grammar  and  jurisprudence  have  a  certain  advantage 
as  means  of  training  the  intellect,  inasmuch  as  they  tax 
pretty  equall}^  all  the  intellectual  powers.  On  this  account 
secondary  education  among  modern  European  nations  is 
based  mainly  upon  the  grammatical  study  of  foreign 
languages.  The  motlier-tongue  and  modern  foreign  lan- 
guages, when  acquired  solely  by  practice,  do  not  call  for 
any  conscious  logical  exercise  of  thought,  though  we  may 
cultivate  by  means  of  them  an  appreciation  for  artistic 
beauty  of  expression.  The  two  classical  languages,  Latin 
and  Grreek,  have,  besides  their  exquisite  logical  subtlety 
and  aesthetic  beauty,  an  additional  advantage,  which  they 
seem  to  possess  in  common  with  most  ancient  and  original 
languages — they  indicate  accurately  the  relations  of  words 
and  sentences  to  each  other  by  numerous  and  distinct 
inflexions.  Languages  are,  as  it  were,  abraded  by  long 
use  ;  grammatical  distinctions  are  cut  down  to  a  mini- 
mum for  the  sake  of  brevity  and  rapidity  of  expression, 
and  are  thus  made  less  and  less  definite,  as  is  obvious  from 
the  comparison  of  any  modern  European  language  with 
Latin  ;  in  English  the  process  has  gone  further  than  in 
any  other.  This  seems  to  me  to  be  really  the  reason  why 
the  modern  languages  are  far  less  fitted  than  the  ancient 
for  instruments  of  education.' 

*  Those  to  whom  German  is  not  a  foreign  tongiie  may,  perhaps,  be  per- 
mitted to  hold  different  views  on  the  efficacy  of  modern  languages  in 
education. — Tb. 


20  ON   THE  RELATION   OF 

As  grammar  is  the  staple  of  school  education,  legal 
studies  are  used,  and  rightly,  as  a  means  of  training  per- 
sons of  maturer  age,  even  when  not  specially  required  for 
professional  purposes. 

We  now  come  to  those  sciences  which,  in  respect  of  the 
kind  of  intellectual  labour  they  require,  stand  at  the  oppo- 
site end  of  the  series  to  philology  and  history  ;  namely,  the 
natural  and  physical  sciences.  I  do  not  mean  to  say  that 
in  many  branches  even  of  these  sciences  an  instinctive 
appreciation  of  analogies  and  a  certain  artistic  sense  have 
no  part  to  play.  On  the  contrary,  in  natural  history  the 
decision  which  characteristics  are  to  be  looked  upon  as 
important  for  classification,  and  which  as  unimportant, 
what  divisions  of  the  animal  and  vegetable  kingdoms  are 
more  natural  than  others,  is  really  left  to  an  instinct  of 
this  kind,  acting  without  any  strictly  definable  rule.  And 
it  is  a  very  suggestive  fact  that  it  was  an  artist,  Groethe, 
who  gave  the  first  impulse  to  the  researches  of  compara- 
tive anatomy  into  the  analogy  of  corresponding  organs  in 
different  animals,  and  to  the  parallel  theory  of  the  meta- 
morphosis of  leaves  in  the  vegetable  kingdom  ;  and  thus, 
in  fact,  really  pointed  out  the  direction  which  the  science 
has  followed  ever  since.  But  even  in  those  departments  of 
science  where  we  have  to  do  with  the  least  understood 
vital  processes  it  is,  speaking  generally,  far  easier  to 
make  out  general  and  comprehensive  ideas  and  prin- 
ciples, and  to  express  them  in  definite  language,  than  in 
cases  where  we  must  base  our  judgment  on  the  analysis  of 
the  human  mind.  It  is  only  when  we  come  to  the  experi- 
mental sciences  to  which  mathematics  are  applied,  and 
especially  when  we  come  to  pure  mathematics,  that  we 
see  the  peculiar  characteristics  of  the  natural  and  physical 
sciences  fully  brought  out. 

The  essential  differentia  of  these  sciences  seems  to  me 
to  consist  in  the  comparative  ease  with  which  the  indi- 


NATURAL   SCIENCE   TO   GENERAL   SCIENCE.  21 

vidual  results  of  observation  and  experiment  are  com- 
bined under  general  laws  of  unexceptionable  validity  and 
of  an  extraordinarily  comprehensive  character.  In  the 
moral  sciences,  on  the  other  hand,  chis  is  just  the  point 
where  insuperable  difficulties  are  encountered.  In  mathe- 
matics the  general  propositions  which,  under  the  name  of 
axioms,  stand  at  the  head  of  the  reasoning,  are  so  few  in 
number,  so  comprehensive,  and  so  immediately  obvious, 
that  no  proof  whatever  is  needed  for  them.  Let  me 
remind  you  that  the  whole  of  algebra  and  arithmetic  is 
developed  out  of  the  three  axioms  : 

'  Things  which  are  equal  to  the  same  things  are  equal 
to  one  another.' 

'  If  equals  be  added  to  equals,  the  wholes  are  equal.' 
*  If  unequals  }je  added  to  equals,  the  wholes  are  unequal.' 
And  the  axioms  of  geometry  and  mechanics  are  not  more 
numerous.  The  sciences  we  have  named  are  developed  out 
of  these  few  axioms  by  a  continual  process  of  deduction 
from  them  in  more  and  more  complicated  cases,  Algebra, 
however,  does  not  confine  itself  to  finding  the  sum  of  the 
most  heterogeneous  combinations  of  a  finite  number  of 
magnitudes,  but  in  the  higher  analysis  it  teaches  us  to 
sum  even  infinite  series,  the  terms  of  which  increase  or 
diminish  according  to  the  most  various  laws  ;  to  solve,  in 
fact,  problems  which  could  never  be  completed  by  direct 
addition.  An  instance  of  this  kind  shows  us  the  conscious 
logical  activity  of  the  mind  in  its  purest  and  most  perfect 
form.  On  the  one  hand  we  see  the  laborious  nature  of 
the  process,  the  extreme  caution  with  which  it  is  necessary 
to  advance,  the  accuracy  required  to  determine  exactly  the 
scope  of  such  universal  principles  as  have  been  attained, 
the  difficulty  of  forming  and  understanding  abstract  con- 
ceptions. On  the  other  hand,  we  gain  confidence  in  the 
certainty,  the  range,  and  the  fertility  of  this  kind  of 
intellectual  work. 


22  ON   THE   RELATION   OF 

The  fertility  of  the  method  comes  out  more  strikingly 
in    applied     mathematics,    especially    in    mathematical 
physics,  including,  of  course,  physical  astronomy.     From 
the   time    when   Newton    discovered,    by   analysing    the 
motions   of   the   planets   on  mechanical   principles,  that 
every   particle    of    ponderable   matter   in    the    universe 
attracts   every  other   particle  with  a   force  varying   in- 
versely as  the   square  of  the  distance,  astronomers  have 
been  able,  in  virtue  of  that  one  law  of  gTavitation,  to 
calculate  with  the   greatest  accuracy  the  movements  of 
the  planets  to  the  remotest  past  and  the  most  distant 
future,  given  only  the  position,  velocity,  and  mass  of  each 
body  of  our  system  at  any  one  time.     More  than  that,  we 
recog-nise  the  operation  of  this  law  in  the  movements  of 
double  stars,  whose  distances  from  us  are  so  great  that 
their  light  takes  years  to  reach  us  ;  in  some  cases,  indeed, 
so  great  that  all  attempts  to  measm'e  them  have  failed. 

This  discovery  of  the  law  of  gravitation  and  its  conse- 
quences is  the  most  imposing  achievement  that  the 
logical  power  of  the  human  mind  has  hitherto  per- 
formed. I  do  not  mean  to  say  that  there  have  not  been 
men  who  in  power  of  abstraction  have  equalled  or  even 
surpassed  Newton  and  the  other  astronomers,  who  either 
paved  the  way  for  his  discovery,  or  have  carried  it  out  to 
its  legitimate  consequences ;  but  there  has  never  been 
presented  to  the  human  mind  such  an  admirable  subject 
as  those  involved  and  complex  movements  of  the  planets, 
which  hitherto  had  served  merely  as  food  for  the  astrolo- 
gical superstitions  of  ignorant  star-gazers,  and  were  now 
reduced  to  a  single  law,  capable  of  rendering  the  most 
exact  account  of  the  minutest  detail  of  their  motions. 

The  principles  of  this  magnificent  discovery  have  been 
successfully  applied  to  several  other  physical  sciences, 
among  which  physical  optics  and  the  theory  of  electricity 
and  magnetism  are  especially  worthy  of  notice.     The  ex- 


NATURAL    SCIENCE   TO    GENERAL    SCIENCE.  23 

perimental  sciences  have  one  great  advantage  over  the 
natural  sciences  in  the  investigation  of  general  laws  of 
nature :  they  can  change  at  pleasure  the  conditions  under 
which  a  given  result  takes  place,  and  can  thus  confine 
themselves  to  a  small  number  of  characteristic  instances, 
in  order  to  discover  the  law.  Of  course  its  validity  must 
then  stand  the  test  of  application  to  more  complex  cases. 
Accordingly  the  physical  sciences,  when  once  the  right 
methods  have  been  discovered,  have  made  proportionately 
rapid  progress.  Not  only  have  they  allowed  us  to  look 
back  into  primaeval  chaos,  where  nebulous  masses  were 
forming  themselves  into  suns  and  planets,  and  becom- 
ing heated  by  the  energy  of  their  contraction  ;  not  only 
have  they  permitted  us  to  investigate  the  chemical  con- 
stituents of  the  solar  atmosphere  and  of  the  remotest 
fixed  stars,  but  they  have  enabled  us  to  turn  the  forces  of 
surrounding  nature  to  our  own  uses  and  to  make  tliem  the 
ministers  of  our  will. 

Enough  has  been  said  to  show  how  widely  the  intel- 
lectual processes  involved  in  this  group  of  sciences  differ, 
for  the  most  part,  from  those  required  by  tne  moral 
sciences.  The  mathematician  need  have  no  memory 
whatever  for  detached  facts,  the  physicist  hardly  any. 
Hypotheses  based  on  the  recollection  of  similar  cases  may, 
indeed,  be  useful  to  guide  one  into  the  right  track,  but 
they  have  no  real  value  till  they  have  led  to  a  precise  and 
strictly  defined  law.  Nature  does  not  allow  us  for  a  moment 
to  doubt  that  we  have  to  do  with  a  rigid  chain  of  cause 
and  effect,  admitting  of  no  exceptions.  Therefore  to  us, 
as  her  students,  goes  forth  the  mandate  to  labour  on  till  we 
have  discovered  unvaiying  laws ;  till  then  we  dare  not  rest 
satisfied,  for  then  only  can  our  knowledge  grapple  victo- 
riously with  time  and  space  and  the  forces  of  the  universe. 

The  iron  labour  of  conscious  logical  reasoning  demands 
great  perseverance  and  great  caution;  it  moves  on  but 


24  ON   THE  RELATION   OF 

slowly,  and  is  rarely  illuminated  by  brilliant  flashes  of 
genius.  It  knows  little  of  that  facility  with  which  the 
most  varied  instances  come  thronging  into  the  memory  of 
the  philologist  or  the  historian.  Eather  is  it  an  essential 
condition  of  the  methodical  progress  of  mathematical 
reasoning  that  the  mind  should  remain  concentrated  on  a 
single  point,  undisturbed  alike  by  collateral  ideas  on  the 
one  hand,  and  by  wishes  and  hopes  on  the  other,  and 
moving  on  steadily  in  the  direction  it  has  deliberately 
chosen.  A  celebrated  logician,  Mr.  John  Stuart  Mill, 
expresses  his  conviction  that  the  inductive  sciences  have 
of  late  done  more  for  the  advance  of  logical  methods  than 
the  labours  of  philosophers  properly  so  called.  One  essen- 
tial ground  for  such  an  assertion  must  undoubtedly  be  that 
in  no  department  of  knowledge  can  a  fault  in  the  chain  of 
reasoning  be  so  easily  detected  by  the  incorrectness  of  the 
results  as  in  those  sciences  in  which  the  results  of  reason- 
ing can  be  most  directly  compared  with  the  facts  of  nature. 
Though  I  have  maintained  that  it  is  in  the  physical 
sciences,  and  especially  in  such  branches  of  them  as  are 
treated  mathematically,  that  the  solution  of  scientific 
problems  has  been  most  successfully  achieved,  you  will 
not,  I  trust,  imagine  that  I  wish  to  depreciate  other 
studies  in  comparison  with  them.  If  the  natural  and 
physical  sciences  have  the  advantage  of  great  perfection 
in  form,  it  is  the  privilege  of  the  moral  sciences  to  deal 
with  a  richer  material,  with  questions  that  touch  more 
nearly  the  interests  and  the  feelings  of  men,  with  the 
human  mind  itself,  in  fact,  in  its  motives  and  the 
different  branches  of  its  activity.  They  have,  indeed, 
the  loftier  and  the  more  difficult  task,  but  yet  they 
cannot  afford  to  lose  sight  of  the  example  of  their  rivals, 
which,  in  form  at  least,  have,  owing  to  the  more  ductile 
nature  of  their  materials,  made  greater  progress.  Not 
only  have  they  something  to  learn  from  them  in  point  of 


N-ATURAL   SCIENCE   TO   GENERAL   SCIENCE.  25 

method,  but  tliey  may  also  draw  encouragement  from 
the  greatness  of  their  results.  And  I  do  think  that  our 
age  has  learnt  many  lessons  from  the  physical  sciences. 
The  absolute,  unconditional  reverence  for  facts,  and  the 
fidelity  with  which  they  are  collected,  a  certain  distrust- 
fulness  of  appearances,  the  effort  to  detect  in  all  cases 
relations  of  cause  and  effect,  and  the  tendency  to  assume 
their  existence,  which  distinguish  our  century  from  pre- 
ceding ones,  seem  to  me  to  point  to  such  an  influence. 

I  do  not  intend  to  go  deeply  into  the  question  how 
far  mathematical  studies,  as  the  representatives  of  con- 
scious logical  reasoning,  should  take  a  more  important 
place  in  school  education.  But  it  is,  in  reality,  one  of 
the  questions  of  the  day.  In  proportion  as  the  range  of 
science  extends,  its  system  and  organisation  must  be 
improved,  and  it  must  inevitably  come  about  that  in- 
dividual students  will  find  themselves  compelled  to  go 
through  a  stricter  course  of  training  than  grammar  is  in 
a  position  to  supply.  What  strikes  me  in  my  own  ex- 
perience of  students  who  pass  from  our  classical  schools 
to  scientific  and  medical  studies,  is  first,  a  certain  laxity 
in  the  application  of  strictly  universal  laws.  The  gram- 
matical rules,  in  which  they  have  been  exercised,  are 
for  the  most  part  followed  by  long  lists  of  exceptions  ; 
accordingly  they  are  not  in  the  habit  of  relying  implicitly 
on  the  certainty  of  a  legitimate  deduction  from  a  strictly 
universal  law.  Secondly,  I  find  them  for  the  most  part 
too  much  inclined  to  trust  to  authority,  even  in  cases 
where  they  might  form  an  independent  judgment.  In 
fact,  in  philological  studies,  inasmuch  as  it  is  seldom 
possible  to  take  in  the  whole  of  the  premisses  at  a  glance, 
and  inasmuch  as  the  decision  of  disputed  questions  often 
depends  on  an  aesthetic  feeling  for  beauty  of  expres- 
sion, and  for  the  genius  of  the  language,  attainable 
only  by  long  training,  it  must  often  happen  that  the 


26  ON  THE   RELATION   OF 

student  is  referred  to  authorities  even  by  the  best 
teachers.  Both  faults  are  traceable  to  a  certain  in- 
dolence and  vagueness  of  thought,  the  sad  effects  of 
which  are  not  confined  to  subsequent  scientific  studies. 
But  certainly  the  best  remedy  for  both  is  to  be  found  in 
mathematics,  where  there  is  absolute  certainty  in  the 
reasoning,  and  no  authority  is  recognised  but  that  of 
one's  own  intelligence. 

So  much  for  the  several  branches  of  science  considered 
as  exercises  for  the  intellect,  and  as  supplementing  each 
other  in  that  respect.  But  knowledge  is  not  the  sole 
object  of  man  upon  earth.  Though  the  sciences  arouse 
and  educate  the  subtlest  powers  of  the  mind,  yet  a  man 
who  should  study  simply  for  the  sake  of  knowing,  would 
assuredly  not  fulfil  the  purpose  of  his  existence.  We 
often  see  men  of  considerable  endowments,  to  whom 
their  good  or  bad  fortune  has  secured  a  comfortable 
livelihood  or  good  social  position,  without  giving  them, 
at  the  same  time,  ambition  or  energy  enough  to  make 
them  work,  dragging  out  a  weary,  unsatisfied  existence, 
while  all  the  time  they  fancy  they  are  following  the 
noblest  aim  of  life  by  constantly  devoting  themselves  to 
the  increase  of  their  knowledge,  and  the  cultivation  of 
their  minds.  Action  alone  gives  a  man  a  life  worth 
living ;  and  therefore  he  must  aim  either  at  the  practical 
application  of  his  knowledge,  or  at  the  extension  of  the 
limits  of  science  itself.  For  to  extend  the  limits  of  science 
is  really  to  work  for  the  progress  of  humanity.  Thus  we 
pass  to  the  second  link,  uniting  the  different  sciences, 
the.  connection,  namely,  between  the  subjects  of  which 
they  treat. 

Knowledge  is  power.  Our  age,  more  than  any  other, 
is  in  a  position  to  demonstrate  the  truth  of  this  maxim. 
We  have  taught  the  forces  of  inanimate  nature  to 
minister  to  the  wants  of  human  life  and  the  designs  of 


NATUEAL    SCIENCE    TO    GENERAL    SCIENCE.  27 

the  human  intellect.  The  application  of  steam  has 
multiplied  our  physical  strength  a  million-fold ;  wea.ving 
and  spinning  machines  have  relieved  us  of  labours,  the 
only  merit  of  which  consisted  in  a  deadening  monotony. 
The  intercourse  between  men,  with  its  far-reaching  in- 
fluence on  material  and  intellectual  progress,  has  increased 
to  an  extent  of  which  no  one  could  have  even  dreamed 
within  the  lifetime  of  the  older  among  us.  But  it  is  not 
merely  on  the  machines  by  which  our  powers  are  multi- 
plied; not  merely  on  rifled  cannon,  and  armour-plated 
ships ;  not  merely  on  accumulated  stores  of  money  and 
the  necessaries  of  life,  that  the  power  of  a  nation  rests ; 
though  these  things  have  exercised  so  unmistakeable  an 
influence,  that  even  the  proudest  and  most  obstinate 
despotisms  of  our  times  have  been  forced  to  think  of 
removing  restrictions  on  industry,  and  of  conceding  to 
the  industrious  middle  classes  a  due  voice  in  their 
counsels.  But  political  organisation,  the  administration 
of  justice,  and  the  moral  discipline  of  individual  citizens 
are  no  less  important  conditions  of  the  preponderance  of 
civilised  nations  ;  and  so  surely  as  a  nation  remains  in- 
accessible to  the  influences  of  civilisation  in  these  respects, 
so  surely  is  it  on  the  high  road  to  destruction.  The 
several  conditions  of  national  prosperity  act  and  react  on 
each  other  ;  where  the  administration  of  justice  is  uncer- 
tain, where  the  interests  of  the  majority  cannot  be  asserted 
by  legitimate  means,  the  development  of  the  national 
resources,  and  of  the  power  depending  upon  them,  is 
impossible  ;  nor  again,  is  it  possible  to  make  good  soldiers 
except  out  of  men  who  have  learnt  under  just  laws  to 
educate  the  sense  of  honour  that  characterises  an  inde- 
pendent man,  certainly  not  out  of  those  who  have  lived 
the  submissive  slaves  of  a  capricious  tyrant. 

Accordingly  every  nation  is  interested  in  the  progress 
of  knowledge  on  the  simple  ground  of  self-preservation, 


28  ON   THE   RELATIO]!^   OF 

even  were  there  no  higlier  wants  of  an  ideal  character  to 
be  satisfied  ;  and  not  merely  in  the  development  of  the 
physical  sciences,  and  their  teclmical  application,  but 
also  in  the  progress  of  legal,  political,  and  moral  sciences, 
and  of  the  accessory  historical  and  philological  studies. 
No  nation  which  would  be  independent  and  influential 
can  afford  to  be  left  behind  in  the  race.  Nor  has  this 
escaped  the  notice  of  the  cultivated  peoples  of  Eiu*ope. 
Never  before  was  so  large  a  part  of  the  public  resources 
devoted  to  universities,  schools,  and  scientific  institutions. 
We  in  Heidelberg  have  this  year  occasion  to  congratu- 
late ourselves  on  another  rich  endowment  granted  by  our 
government  and  our  parliament. 

I  was  speaking,  at  the  beginning  of  my  address,  of  the 
increasing  division  of  labour  and  the  improved  organisa- 
tion among  scientific  workers.  In  fact,  men  of  science 
form,  as  it  were,  an  organised  army,  labouring  on  behalf 
of  the  whole  nation,  and  generally  under  its  direction 
and  at  its  expense,  to  augment  the  stock  of  such  know- 
ledge as  may  serve  to  promote  industrial  enterprise,  to 
increase  wealth,  to  adorn  life,  to  improve  political  and 
social  relations,  and  to  further  the  moral  development  of 
individual  citizens.  After  the  immediate  practical  re- 
sults of  their  work  we  forbear  to  inquire ;  that  we  leave 
to  the  uninstructed.  We  are  convinced  that  whatever 
contributes  to  the  knowledge  of  the  forces  of  nature  or 
the  powers  of  the  human  mind  is  worth  cherishing,  and 
may,  in  its  own  due  time,  bear  practical  fruit,  very  often 
where  we  should  least  have  expected  it.  Who,  when 
Galvani  touched  the  muscles  of  a  frog  with  different 
metals,  and  noticed  their  contraction,  could  have  dreamt 
that  eighty  years  afterwards,  in  virtue  of  the  self-same 
process,  whose  earliest  manifestations  attracted  his  at- 
tention in  his  anatomical  researches,  all  Europe  would 
be  traversed  with  wires,  flashing  intelligence  from  Madrid 


NATUEAL   SCIENCE   TO   GENEEAL   SCIENCE.  29 

to  St.  Petersburg  witli  the  speed  of  lightning  ?  In  the 
hands  of  Gralvani,  and  at  first  even  in  Volta's,  electrical 
currents  were  phenomena  capable  of  exerting  only  the 
feeblest  forces,  and  could  not  be  detected  except  by  the 
most  delicate  apparatus.  Had  they  been  neglected,  on 
the  ground  that  the  investigation  of  them  promised  no 
immediate  practical  result,  we  should  now  be  ignorant  of 
the  most  important  and  most  interesting  of  the  links 
between  the  various  forces  of  nature.  When  young 
Gralileo,  then  a  student  at  Pisa,  noticed  one  day  during 
divine  service  a  chandelier  swinging  backwards  and  for- 
wards, and  convinced  himself,  by  counting  his  pulse,  that 
the  duration  of  the  oscillations  was  independent  of  the 
arc  through  which  it  moved,  who  could  know  that  this 
discovery  would  eventually  put  it  in  our  power,  by  means 
of  the  pendulum,  to  attain  an  accuracy  in  the  measure- 
ment of  time  till  then  deemed  impossible,  and  would 
enable  the  storm-tossed  seaman  in  the  most  distant  oceans 
to  determine  in  what  degree  of  longitude  he  was  sailing  ? 
Whoever,  in  the  pursuit  of  science,  seeks  after  imme- 
diate practical  utility,  may  generally  rest  assured  that  he 
will  seek  in  vain.  All  that  science  can  achieve  is  a  perfect 
knowledge  and  a  perfect  understanding  of  the  action  of 
natural  and  moral  forces.  Each  individual  student  must 
be  content  to  find  his  reward  in  rejoicing  over  new  dis- 
coveries, as  over  new  victories  of  mind  over  reluctant 
matter,  or  in  enjoying  the  aesthetic  beauty  of  a  well- 
ordered  field  of  knowledofe,  where  the  connection  and  the 
filiation  of  every  detail  is  clear  to  the  mind,  and  where  all 
denotes  the  presence  of  a  ruling  intellect ;  he  must  rest 
satisfied  with  the  consciousness  that  he  too  has  contributed 
something  to  the  increasing  fund  of  knowledge  on  which 
the  dominion  of  man  over  all  the  forces  hostile  to  intelli- 
gence reposes.  He  will,  indeed,  not  always  be  permitted 
to  expect  from  his  fellow-men  appreciation  and  reward 


30  ON   THE   EELATIOIS"   OF 

adequate  to  the  value  of  his  work.  It  is  only  too  true, 
that  many  a  man  to  whom  a  monument  has  been  erected 
after  his  death,  would  have  been  delighted  to  receive 
during  his  lifetime  a  tenth  part  of  the  money  spent  in 
doing  honour  to  his  memory.  At  the  same  time,  we  must 
acknowledge  that  the  value  of  scientific  discoveries  is  now 
far  more  fully  recognised  than  formerly  by  public  opinion, 
and  that  instances  of  the  authors  of  great  advances  in 
science  starving  in  obscurity  have  become  rarer  and  rarer. 
On  the  contrary,  the  governments  and  peoples  of  Europe 
have,  as  a  rule,  admitted  it  to  be  their  duty  to  recompense 
distinguished  achievements  in  science  by  appropriate  ap- 
pointments or  special  rewards. 

The  sciences  have  then,  in  this  respect,  all  one  common 
aim,  to  establish  the  supremacy  of  intelligence  over  the 
world  :  while  the  moral  sciences  aim  directly  at  making 
the  resources  of  intellectual  life  more  abundant  and  more 
interesting,  and  seek  to  separate  the  pure  gold  of  Truth 
from  alloy,  the  physical  sciences  are  striving  indirectly 
towards  the  same  goal,  inasmuch  as  they  labour  to  make 
mankind  more  and  more  independent  of  the  material  re- 
straints that  fetter  their  activity.  Each  student  works  in 
his  own  department,  he  chooses  for  himself  those  tasks  for 
which  he  is  best  fitted  by  his  abilities  and  his  training. 
But  each  one  must  be  convinced  that  it  is  only  in  connec- 
tion with  others  that  he  can  further  the  great  work,  and 
that  therefore  he  is  bound,  not  only  to  investigate,  but  to 
do  his  utmost  to  make  the  results  of  his  investigation 
completely  and  easily  accessible.  If  he  does  this,  he  will 
derive  assistance  from  others,  and  will  in  his  turn  be  able 
to  render  them  his  aid.  The  annals  of  science  abound  in 
evidence  how  such  mutual  services  have  been  exchanged, 
even  between  departments  of  science  apparently  most 
remote.  Historical  chronology  is  essentially  based  on 
astronomical  calculations  of  eclipses,  accounts  of  which 


NATUEAL   SCIENCE   TO   GENEEAL   SCIENCE.  31 

are  preserved  in  ancient  histories.  Conversely,  many  of 
the  important  data  of  astronomy — for  instance,  the  in- 
variability of  the  length  of  the  day,  and  the  periods  of 
several  comets — rest  upon  ancient  historical  notices.  Of 
late  years,  physiologists,  especially  Briicke,  have  actually 
undertaken  to  draw  Up  a  complete  system  of  all  the 
vocables  that  can  be  produced  by  the  organs  of  speech, 
and  to  base  upon  it  propositions  for  an  universal  alphabet, 
adapted  to  all  human  languages.  Thus  physiology  has 
entered  the  service  of  comparative  philology,  and  has 
already  succeeded  in  accounting  for  many  apparently 
anomalous  substitutions,  on  the  ground  that  they  are 
governed,  not  as  hitlierto  supposed,  by  the  laws  of  eu- 
phony, but  by  similarity  between  the  movements  of  the 
mouth  that  produce  them.  Again,  comparative  philo- 
logy gives  us  information  about  the  relationships,  the 
separations  and  the  migrations  of  tribes  in  prehistoric 
times,  and  of  the  degree  of  civilisation  which  they  had 
reached  at  the  time  when  they  parted.  For  the  names  of 
objects  to  which  they  had  already  learnt  to  give  distinc- 
tive appellations  reappear  as  words  common  to  their  later 
languages.  So  that  the  study  of  languages  actually  gives 
us  historical  data  for  periods  respecting  which  no  other 
historical  evidence  exists.^  Yet  again  I  may  notice  the 
help  which  not  only  the  sculptor,  but  the  archaeologist, 
concerned,  with  the  investigation  of  ancient  statues, 
derives  from  anatomy.  And  if  I  may  be  permitted  to 
refer  to  my  own  most  recent  studies,  I  would  mention 
that  it  is  possible,  by  reference  to  physical  acoustics 
and  to  the  physiological  theory  of  the  sensation  of  hear- 
ing, to  account  for  the  elementary  principles  on  which 
our  musical  system  is  constructed,  a  problem  essentially 
within  the  sphere  of  sesthetics.  In  fact^  it  is  a  general 
principle  that  the  physiology  of  the  organs  of  sense  is 

^  See,  for  example,  Mommsen's  Borne,  Book  I.  ch.  ii. — Tjr. 


32  ON-  THE   RELATION   OF   NATURAL   SCIENCE. 

most  intimately  connected  with  psychology,  inasmuch  as 
physiology  traces  in  our  sensations  the  results  of  mental 
processes  which  do  not  fall  within  the  sphere  of  con- 
ciousness,  and  must  therefore  have  remained  inaccessible 
to  us. 

I  have  been  able  to  quote  only  some  of  the  most 
striking  instances  of  this  interdependence  of  different 
sciences,  and  such  as  could  be  explained  in  a  few  words. 
Naturally,  too,  I  have  tried  to  choose  them  from  the  most 
widely-separated  sciences.  But  far  wider  is  of  course  the 
influence  which  allied  sciences  exert  upon  each  other. 
Of  that  I  need  not  speak,  for  each  of  you  knows  it  from 
his  own  experience. 

In  conclusion,  I  would  say,  let  each  of  us  think  of  him- 
self, not  as  a  man  seeking  to  gratify  his  own  thirst  for 
knowledge,  or  to  promote  his  own  private  advantage,  or 
to  shine  by  his  own  abilities,  but  rather  as  a  fellow- 
labourer  in  one  great  common  work  bearing  upon  the 
highest  interests  of  humanity.  Then  assuredly  we  shall 
not  fail  of  our  reward  in  the  approval  of  our  own  con- 
science and  the  esteem  of  our  fellow-citizens.  To  keep 
up  these  relations  between  all  searchers  after  truth  and 
all  branches  of  kno"wledge,  to  animate  them  all  to  vigo- 
rous co-operation  towards  their  common  end,  is  the  great 
office  of  the  Universities.  Therefore  is  it  necessary  that 
the  four  Faculties  should  ever  go  hand  in  hand,  and  in 
this  conviction  will  we  strive,  so  far  as  in  us  lies,  to  press 
onward  to  the  fulfilment  of  our  great  mission. 


ON 

GOETHE'S  SCIENTIFIC  RESEARCHES. 

A  LECTURE  DELIVERED  BEFORE   THE   GERMAIN   SOCIETY   OP 
KONIGSBERG,   IN   THE   SPRING   OE  1853. 


It  could  not  but  be  that  Groethe,  whose  comprehensive 
genius  was  most  strikingly  apparent  in  that  sober  clear- 
ness with  which  he  grasped  and  reproduced  with  lifelike 
freshness  the  realities  of  nature  and  human  life  in  their 
minutest  details,  should,  by  those  very  qualities  of  his 
mind,  be  drawn  towards  the  study  of  physical  science. 
And  in  that  department,  he  was  not  content  with  ac- 
quiring what  others  could  teach  him,  but  he  soon  at- 
tempted, as  so  original  a  mind  was  sure  to  do,  to  strike 
out  an  independent  and  a  very  characteristic  line  of 
thought.  He  directed  his  energies,  not  only  to  the 
descriptive,  but  also  to  the  experimental  sciences ;  the 
chief  results  being  his  botanical  and  osteological  treatises 
on  the  one  hand,  and  his  theory  of  colour  on  the  other. 
The  first  germs  of  these  researches  belong  for  the  most 
part  to  the  last  decade  of  the  eighteenth  century,  though 
some  of  them  were  not  completed  nor  published  till  later. 
Since  that  time  science  has  not  only  made  great  progress, 
but  has  widely  extended  its  range.  It  has  assumed  in 
some  respects  an  entirely  new  aspect,  it  has  opened  out 


34         ON  Goethe's  scientific  researches. 

new  fields  of  research  and  undergone  many  changes  in  its 
theoretical  views.  I  shall  attempt  in  the  following 
Lecture  to  sketch  the  relation  of  Goethe's  researches  to 
the  present  stand-point  of  science,  and  to  bring  out  the 
guiding  idea  that  is  common  to  them  all. 

Tlie  peculiar  character  of  the  descrijDtive  sciences — 
botany,  zoology,  anatomy,  and  the  like — is  a  necessary 
result  of  the  work  imposed  upon  them.  They  undertake 
to  collect  and  sift  an  enormous  mass  of  facts,  and,  above 
all,  to  bring  them  into  a  logical  order  or  system.  Up  to 
this  point  their  work  is  only  the  dry  task  of  a  lexico- 
grapher ;  their  system  is  nothing  more  than  a  muniment- 
room  in  which  the  accumulation  of  papers  is  so  arranged 
that  any  one  can  find  what  he  wants  at  any  moment. 
The  more  intellectual  part  of  their  work  and  their  real 
interest  only  begins  when  they  attempt  to  feel  after  the 
scattered  traces  of  law  and  order  in  the  disjointed,  hetero- 
geneous mass,  and  out  of  it  to  construct  for  themselves  an 
orderly  system,  accessible  at  a  glance,  in  which  every 
detail  has  its  due  place,  and  gains  additional  interest  from 
its  connection  with  the  whole. 

In  such  studies,  both  the  organising  capacity  and  the 
insight  of  our  poet  found  a  congenial  sphere — the  epoch 
was  moreover  propitious  to  him.  He  found  ready  to 
his  hand  a  sufficient  store  of  logically  arranged  mate- 
rials in  botany  and  comparative  anatomy,  copious  and 
systematic  enough  to  admit  of  a  comprehensive  view, 
and  to  indicate  the  way  to  some  happy  glimpse  of  an 
all-pervading  law ;  while  his  contemporaries,  if  they  made 
any  efforts  in  this  direction,  wandered  without  a  com- 
pass, or  else  they  were  so  absorbed  in  the  dry  registra- 
tion of  facts,  that  they  scarcely  ventured  to  think  of 
anything  beyond.  It  was  reserved  for  Goethe  to  intro- 
duce two  ideas  of  infinite  fruitfulness. 

The  first  was  the  conception  that  the  differences  in  the 


ON  goethe's  scientific  researches.         35 

anatomy  of  different  animals  are  to  be  looked  upon  as 
variations  from  a  common  phase  or  type,  induced  by  dif- 
ferences of  habit,  locality,  or  food.  The  observation 
which  led  him  to  this  fertile  conception  was  by  no  means 
a  striking  one  ;  it  is  to  be  found  in  a  monograph  on  the 
intermaxillary  bone,  written  as  early  as  1786.  It  was 
known  that  in  most  vertebrate  animals  (that  is,  mam- 
malia, birds,  amphibia,  and  fishes)  the  upper  jaw  consists 
of  two  bones,  the  upper  jaw-bone  and  the  intermaxillary 
bone.  The  former  always  contains  in  the  mammalia  the 
molar  and  the  canine  teeth,  the  latter  the  incisors.  Man, 
who  is  distinguished  from  all  other  animals  by  the  ab- 
sence of  the  projecting  snout,  has,  on  the  contrary,  on 
each  side  only  one  bone,  the  upper  jaw-bone,  containing 
all  the  teeth.  This  being  so,  Groethe  discovered  in  the 
human  skull  faint  traces  of  the  sutures,  which  in  animals 
unite  the  upper  and  middle  jaw-bones,  and  concluded 
from  it  that  man  had  originally  possessed  an  inter- 
maxillary bone,  which  had  subsequently  coalesced  with 
the  upper  jaw-bone.  This  obscure  fact  opened  up  to  him 
a  source  of  the  most  intense  interest  in  the  field  of  osteo- 
logy, generally  so  much  decried  as  the  driest  of  studies. 
That  details  of  structure  should  be  the  same  in  man  and 
in  animals  when  the  parts  continue  to  perform  similar 
functions  had  involved  nothing  extraordinary.  In  fact, 
Camper  had  already  attempted,  on  this  principle,  to  trace 
similarities  of  structure  even  between  man  and  fishes. 
But  the  persistence  of  this  similarity,  at  least  in  a  rudi- 
mentary form,  even  in  a  case  when  it  evidently  does  not 
correspond  to  any  of  the  requirements  of  the  complete 
human  structure,  and  consequently  needs  to  be  adapted 
to  them  by  the  coalescence  of  two  parts  originally  sepa- 
rate, was  what  struck  Groethe's  far-seeing  eye,  and  sug- 
gested to  him  a  far  more  comprehensive  view  than  had 
hitherto  been  taken.  Fui-ther  studies  soon  convinced 
3 


36         ON  Goethe's  scientific  rese.4Eches. 

liim  of  the  universality  of  his  newly-discovered  principle, 
so  that  in  1795  and  1796  he  was  able  to  define  more 
clearly  the  idea  that  had  struck  him  in  1786,  and  to 
commit  it  to  writing  in  his  '  Sketch  of  a  Greneral  Intro- 
duction to  Comparative  Anatomy.'  He  there  lays  down 
with  the  utmost  confidence  and  precision,  that  all  differ- 
ences in  the  structure  of  animals  must  be  looked  upon  a^ 
variations  of  a  single  primitive  type,  induced  by  the 
coalescence,  the  alteration,  the  increa-se,  the  diminution, 
or  even  the  complete  removal  of  single  parts  of  the 
structure  ;  the  very  principle,  in  fact,  which  has  become 
the  leading  idea  of  comparative  anatomy  in  its  present 
stage.  Nowhere  has  it  been  belter  or  more  clearly  ex- 
pressed than  in  Goethe's  writings.  Subsequent  authorities 
have  made  but  few  essential  alterations  in  his  theory. 
Tije  most  important  of  these  is,  that  we  no  longer  under- 
take to  construct  a  common  type  for  the  whole  animal 
kingdom,  but  are  content  with  one  for  each  of  Cuvier's 
great  divisions.  The  industry  of  Goethe's  successors  has 
accumulated  a  well-sifted  stock  of  facts,  infinitely  more 
copious  than  what  he  could  command,  and  has  followed 
up  successfully  into  the  minutest  details  what  he  could 
only  indicate  in  a  general  way. 

The  second  leading  conception  which  science  owes  to 
Goethe  enunciated  the  existence  of  an  analogy  between 
the  different  parts  of  one  and  the  same  organic  being", 
similar  to  that  which  we  have  just  pointed  out  as  sub- 
sisting between  corresponding  parts  of  different  species. 
In  most  organisms  we  see  a  great  repetition  of  single 
parts.  This  is  most  striking  in  the  vegetable  kingdom ; 
each  plant  has  a  great  number  of  similar  stem  leaves, 
similar  petals,  similar  stamens,  and  so  on.  According  to 
Goethe's  own  account,  the  idea  first  occurred  to  him  while 
looking  at  a  fan-palm  at  Padua.  He  was  struck  by  the 
immense  variety   of   changes    of    form   which    the    sue- 


ox  Goethe's  scientific  reseaeches.         37 

cessively-developed  stem-leaves  exhibit,  by  the  way  in 
which  the  first  simple  root  leaflets  are  replaced  by  a  series 
of  more  and  more  divided  leaves,  till  we  come  to  the  most 
complicated. 

He  afterwards  succeeded  in  discoveringf  the  transforma- 
tion  of  stem-leaves  into  sepals  and  petals,  and  of  sepals 
and  petals  into  stamens,  nectaries,  and  ovaries,  and  thus 
he  was  led  to  the  doctrine  of  the  metamorphosis  of  plants, 
which  he  published  in  1790.  Just  as  the  anterior  extre- 
mity of  vertebrate  animals  takes  different  forms,  becoming 
in  man  and  in  apes  an  arm,  in  other  animals  a  paw  with 
claws,  or  a  forefoot  with  a  hoof,  or  a  fin,  or  a  wing,  but 
always  retains  the  same  divisions,  the  same  position,  and 
the  same  connection  with  the  trunk,  so  the  leaf  appears 
as  a  cotyledon,  stem-leaf,  sepal,  petal,  stamen,  nectary, 
ovary,  &c.,  all  resembling  each  other  to  a  certain  extent 
in  origin  and  composition,  and  even  capable,  under 
certain  unusual  conditions,  of  passing  from  one  form  into 
the  other,  as,  for  example,  may  be  seen  by  any  one  who 
looks  carefully  at  a  full-blown  rose,  where  some  of  the 
stamens  are  completely,  some  of  them  partially,  changed 
into  petals.  This  view  of  Groethe's,  like  the  other,  is  now 
completely  adopted  into  science,  and  enjoys  the  universal 
assent  of  botanists,  though  of  course  some  details  are  still 
matters  of  controversy,  as,  for  instance,  whether  the  bud 
is  a  single  leaf  or  a  branch. 

In  the  animal  kingdom,  the  composition  of  an  indi- 
vidual out  of  several  similar  parts  is  very  striking  in  the 
great  sub-kingdom  of  the  articulata — for  example,  in 
insects  and  worms.  The  larva  of  an  insect,  or  the  cater- 
pillar of  a  butterfly,  consists  of  a  number  of  perfectly 
similar  segments  ;  only  the  first  and  last  of  them  differ, 
and  that  but  slightly,  from  the  others.  After  their 
transformation  into  perfect  insects,  they  furnish  clear  and 
simple  exemplifications  of  the  view  which   Groethe  had 


38         ON  goethe's  scientific  reseaeches. 

grasped  in  his  doctrine  of  the  metamorphosis  of  plants, 
the  development,  namely,  of  apparently  very  dissimilar 
forms  from  parts  originally  alike.  The  posterior  seg- 
ments retain  their  original  simple  form  ;  those  of  the 
breast-plate  are  drawn  closely  together,  and  develop  feet 
and  wings  ;  while  those  of  the  head  develop  jaws  and 
feelers ;  so  that  in  the  perfect  insect,  the  original  seg- 
ments are  recognised  only  in  the  posterior  part  of  the 
body.  In  the  vertebrata,  again,  a  repetition  of  similar 
parts  is  suggested  by  the  vertebral  column,  but  has  ceased 
to  be  observable  in  the  external  form.  A  fortunate  glance 
at  a  broken  sheep's  skull,  which  Groethe  found  by  acci- 
dent on  the  sand  of  the  Lido  at  Venice,  suggested  to  him 
that  the  skull  itself  consisted  of  a  series  of  very  much 
altered  vertebrfE.  At  first  sight,  no  two  things  can  be 
more  unlike  than  the  broad  uniform  cranial  cavity  of  the 
mammalia,  inclosed  by  smooth  plates,  and  the  narrow 
cvlindrical  tube  of  the  spinal  marrow,  composed  of  short, 
massy,  jagged  bones.  It  was  a  bright  idea  to  detect  the 
transformation  in  the  skull  of  a  mammal ;  the  similarity 
is  more  striking  in  the  amphibia  and  fishes.  It  should 
be  added  that  Groethe  left  this  idea  unpublished  for  a 
long  time,  apparently  because  he  was  not  quite  sure  how 
it  would  be  received.  Meantime,  in  1806,  the  same  idea 
occurred  to  Oken,  who  introduced  it  to  the  scientific 
world,  and  afterwards  disputed  with  G-oethe  the  priority 
of  discovery.  In  fact,  Goethe  had  waited  till  1817,  when 
the  opinion  had  begun  to  find  adherents,  and  then  de- 
clared that  he  had  had  it  in  his  mind  for  thirty  years. 
Up  to  the  present  day,  the  number  and  composition  of 
the  vertebrae  of  the  skull  are  a  subject  of  controversy, 
but  the  principle  has  maintained  its  ground. 

Goethe's  views,  however,  on  the  existence  of  a  common 
type  in  the  animal  kingdom  do  not  seem  to  have  exercised 
any  direct  influence  on  the   progress  of  science.      The 


ON  Goethe's  scientific  rese.\rches.         39 

doctrine  of  the  metamorphosis  of  plants  was  introduced 
into  botany  as  his  distinct  and  recognised  property  ;  but 
his  views  on  osteology  were  at  first  disputed  by  ana- 
tomists, and  only  subsequently  attracted  attention  when 
the  science  had,  apparently  on  independent  grounds, 
found  its  way  to  the  same  discovery.  He  himself  com- 
plains that  his  first  ideas  of  a  common  type  had  en- 
countered nothing  but  contradiction  and  scepticism  at 
the  time  when  he  was  working  them  out  in  his  own  mind, 
and  that  even  men  of  the  freshest  and  most  original 
intellect,  like  the  two  Von  Humboldts,  had  listened  to 
them  with  something  like  impatience.  But  it  is  almost 
a  matter  of  course  that  in  any  natural  or  physical  science, 
theoretical  ideas  attract  the  attention  of  its  cultivators 
only  when  they  are  advanced  in  connection  with  the 
whole  of  the  evidence  on  which  they  rest,  and  thus  justify 
their  title  to  recognition.  Be  that  as  it  may,  Groethe  is 
entitled  to  the  credit  of  having  caught  the  first  glimpse 
of  the  guiding  ideas  to  which  the  sciences  of  botany  and 
anatomy  were  tending,  and  by  which  their  present  form 
is  determined. 

But  great  as  is  the  respect  which  Groethe  has  secured 
by  his  achievements  in  the  descriptive  natural  sciences, 
the  denunciation  heaped  by  all  physicists  on  his  re- 
searches in  their  department,  and  especially  on  his 
'  theory  of  colour,'  is  at  least  as  uncompromising.  This 
is  not  the  place  to  plunge  into  the  controversy  that 
raged  on  the  subject,  and  so  I  shall  only  attempt  to  state 
clearly  the  points  at  issue,  and  to  explain  what  prin- 
ciple was  involved,  and  what  is  the  latent  significance 
of  the  dispute. 

To  this  end  it  is  of  some  importance  to  go  back  to  the 
history  of  the  origin  of  the  theory,  and  to  its  simplest 
form,  because  at  that  stage  of  the  controversy  the 
points  at  issue  are  obvious,  and  admit  of  easy  and  dis- 


40         ON  Goethe's  scientific  rese.\kches. 

tinct   statement,   unencumbered   by    disputes  about   the 
correctness  of  detached  facts  and  complicated  theories. 

Groethe  himself  describes  veiy  gracefully,  in  the  con- 
fession at  the  end  of  his  '  Theory  of  Colour,'  how  he  came 
to  take  up  the  subject.  Finding  himself  unable  to  grasp 
the  aesthetic  principles  involved  in  effects  of  colour,  he 
resolved  to  resume  the  study  of  the  physical  theory,  which 
he  had  been  taught  at  the  university,  and  to  repeat  for 
himself  the  experiments  connected  with  it.  With  that 
view  he  borrowed  a  prism  of  Hofrath  Biitter,  of  Jena,  but 
was  prevented  by  other  occupations  from  carrying  out  his 
plan,  and  kept  it  by  him  for  a  long  time  unused.  The 
owner  of  the  prism,  a  very  orderly  man,  after  several 
times  asking  in  vain,  sent  a  messenger  with  instructions 
to  bring  it  back  directly.  Goethe  took  it  out  of  the  case, 
and  thought  he  would  take  one  more  peep  through  it.  To 
make  certain  of  seeing  something,  he  turned  it  towards  a 
long  white  wall,  under  the  impression  that  as  there  was 
plenty  of  light  there  he  could  not  fail  to  see  a  brilliant 
example  of  the  resolution  of  light  into  different  colours  ; 
a  supposition,  by  the  way,  which  shows  how  little  Newton's 
theory  of  the  phenomena  was  then  present  to  his  mind. 
Of  course  he  was  disappointed.  On  the  white  wall  he  saw 
no  colours  ;  they  only  appeared  where  it  was  bounded  by 
darker  objects.  Accordingly  he  made  the  observation — 
which,  it  should  be  added,  is  fully  accounted  for  by 
Newton's  theory — that  colour  can  only  be  seen  through  a 
prism  where  a  dark  object  and  a  bright  one  have  the  same 
boundary.  Struck  by  this  observation,  which  was  quite 
new  to  him,  and  convinced  that  it  was  irreconcilable  with 
Newton's  theory,  he  induced  the  owner  of  the  prism  to 
relent,  and  devoted  himself  to  the  question  with  the 
utmost  zeal  and  interest.  He  prepared  sheets  of  paper 
with  black  and  white  spaces,  and  studied  the  phenomenon 
under  every  variety  of  condition,  until  he  thought  he  had 


ON  Goethe's  scientific  eeseaeches.         41 

sufficiently  proved  his  rules.  He  next  attempted  to  ex- 
plain his  supposed  discovery  to  a  neighbour,  who  was  a 
physicist,  and  was  disagreeably  surprised  to  be  assured  by 
him  that  the  experiments  were  well  known,  and  fully 
accounted  for  in  Newton's  theory.  Every  other  natural 
philosopher  whom  he  consulted  told  him  exactly  the  same, 
including  even  the  brilliant  Lichtenberg,  whom  he  tried 
for  a  long  time  to  convert,  but  in  vain.  He  studied 
Newton's  writing's,  and  fancied  he  had  found  some  falla- 
cies in  them  which  accounted  for  the  error.  Unable  to 
convince  any  of  his  acquaintances,  he  at  last  resolved  to 
appear  before  the  bar  of  public  opinion,  and  in  1791  and 
1792  published  the  first  and  second  paits  of  his  'Contri- 
butions to  Physical  Optics,' 

In  that  work  he  describes  the  appearances  presented  by 
white  discs  on  a  black  ground,  black  discs  on  a  white 
gTound,  and  coloured  discs  on  a  black  or  white  ground, 
when  examined  through  a  prism.  As  to  the  results  of 
the  experiments  there  is  no  dispute  whatever  between  him 
and  the  physicists.  He  describes  the  phenomena  he  saw 
with  great  truth  to  nature  ;  the  style  is  lively,  and  the 
arrangement  such  as  to  make  a  conspectus  of  them  easy 
and  inviting  ;  in  short,  in  this  as  in  all  other  cases  where 
facts  are  to  be  described,  he  proves  himself  a  master.  At 
the  same  time  he  expresses  his  conviction  that  the  facts 
he  has  adduced  are  calculated  to  refute  Newton's  theory. 
There  are  two  points  especially  which  he  considers  fatal  to 
it :  first,  that  the  centre  of  a  broad  white  surface  remains 
white  when  seen  through  a  prism  ;  and  secondly,  that 
even  a  black  streak  on  a  white  gTOund  can  be  entirely 
decomposed  into  colours. 

Newton's  theory  is  based  on  the  hypothesis  that  there 
exists  light  of  different  kinds,  distinguished  from  one 
another  by  the  sensation  of  colour  which  they  produce  in 
the  eye.     Thus  there  is  red,  orange,  yellow,  gi-een,  blue, 


42  ON   GOETHE  S   SCIENTIFIC  EESEAKCHES. 

and  violet  light,  and  light  of  all  intermediate  colours. 
Different  kinds  of  light,  or  differently  colom-ed  lights, 
produce,  when  mixed,  derived  colours,  which  to  a  cer- 
tain extent  resemble  the  original  colours  from  which 
they  are  derived  ;  to  a  certain  extent  form  new 
tints.  White  is  a  mixture  of  all  the  before-named 
colours  in  certain  definite  proportions.  But  the  pri- 
mitive colours  can  always  be  reproduced  by  analysis 
from  derived  colom*s,  or  from  white,  while  themselves 
incapable  of  analysis  or  change.  The  cause  of  the  colours 
of  transparent  and  opaque  bodies  is,  that  when  white  light 
falls  upon  them  they  destroy  some  of  its  constituents  and 
send  to  the  eye  other  constituents,  but  no  longer  mixed 
in  the  right  proportions  to  produce  white  light.  Thus  a 
piece  of  red  glass  looks  red,  because  it  transmits  only  red 
rays.  Consequently  all  colour  is  derived  solely  from  a 
change  in  the  proportions  in  which  light  is  mixed,  and  is, 
therefore,  a  property  of  light,  not  of  the  coloured  bodies, 
which  only  furnish  an  occasion  for  its  manifestation. 

A  prism  refracts  transmitted  light ;  that  is  to  say,  de- 
flects it  so  that  it  makes  a  certain  angle  with  its  original 
direction  ;  the  rays  of  simple  light  of  diflferent  colours 
have,  according  to  Newton,  different  refrangibilities,  and 
therefore,  after  refraction  in  the  prism,  pm'sue  different 
com'ses  and  separate  from  each  other.  Accordingly  a 
luminous  point  of  infinitely  small  dimensions  appearSj 
when  seen  through  the  prism,  to  be  first  displaced,  and 
secondly,  extended  into  a  coloured  line,  the  so-called 
prismatic  spectrum,  which  shows  what  are  called  the  pri- 
mary colours  in  the  order  above-named.  If,  however,  you 
look  at  a  broader  luminous  surface,  the  spectra  of  the 
points  near  the  middle  are  superposed,  as  may  be  seen 
from  a  simple  geometrical  investigation,  in  such  pro- 
portions as  to  give  white  light,  except  at  the  edges,  where 
certain  of  the  colours  are  free.  This  white  surface  appears 
displaced,  as  the  luminous  point  did ;  but  instead  of  being 


ON  Goethe's  scientific  reseakches.         43 

coloui'ed  throughout,  it  has  on  one  side  a  margin  of  blue 
and  violet,  on  the  other  a  margin  of  red  and  yellow.  A 
black  patch  between  two  bright  surfaces  may  be  entirely 
covered  by  their  coloured  edges ;  and  when  these  spectra 
meet  in  the  middle,  the  red  of  the  one  and  the  violet  of 
the  other  combine  to  form  purple.  Thus  the  colours  into 
which,  at  first  sight,  it  seems  as  if  the  black  were  analysed 
are  in  reality  due,  not  to  the  black  strip,  but  to  the  white 
on  each  side  of  it. 

It  is  evident  that  at  the  lirst  moment  Goethe  did  not 
recollect  Newton's  theory  well  enough  to  be  able  to  find 
out  the  physical  explanation  of  the  facts  I  have  just 
glanced  at.  It  was  afterwards  laid  before  him  again  and 
again,  and  that  in  a  thoroughly  intelligible  form,  for  he 
speaks  about  it  several  times  in  terms  that  show  he  under- 
stood it  quite  correctly.  But  he  is  still  so  dissatisfied  with 
it,  that  he  persists  in  his  assertion  that  the  facts  just  cited 
are  of  a  nature  to  convince  any  one  who  observes  them  of 
the  absolute  incorrectness  of  Newton's  theory.  Neither 
here  nor  in  his  later  controversial  writings  does  he  ever 
clearly  state  in  what  he  conceives  the  insufficiency  of  the 
explanation  to  consist.  He  merely  repeats  again  and  again 
that  it  is  quite  absurd.  And  yet  I  cannot  see  how  any  one, 
whatever  his  views  about  colour,  can  deny  that  the  theory 
is  perfectly  consistent  with  itself;  and  that  if  the  hypo- 
thesis from  which  it  starts  be  granted,  it  explains  the 
observed  facts  completely  and  even  simply.  Newton  him- 
self mentions  these  spurious  spectra  in  several  passages  of 
his  optical  works,  without  going  into  any  special  eluci- 
dation of  the  point,  considering,  of  course,  that  the 
explanation  follows  at  once  from  his  hypothesis.  And  he 
seems  to  have  had  good  reason  to  think  so ;  for  Groethe  no 
sooner  began  to  call  the  attention  of  his  scientific  friends 
to  the  phenomena,  than  all  with  one  accord,  as  he  himself 
tells  us,  met  his  difficulties  with  this  explanation  from 
Newton's  principles,  which,  though    not  actually  in  his 


44         0]^  Goethe's  scientific  researches. 

writings,  instantly  suggested  itself  to  every  one  who  knew 
them. 

A  reader  who  tries  to  realise  attentively  and  thoroughly 
every  step  in  this  part  of  the  controversy  is  apt  to  expe- 
rience at  this  point  an  uncomfortable,  almost  a  painful 
feeling  to  see  a  man  of  extraordinary  abilities  persist- 
ently declaricg  that  there  is  an  obvious  absurdity  lurking 
in  a  few  inferences  apparently  quite  clear  and  simple. 
He  searches  and  searches,  and  at  last  unable,  with 
all  his  efforts,  to  find  any  such  absm'dity,  or  even  the 
appearance  of  it,  he  gets  into  a  state  of  mind  in  which 
his  own  ideas  are,  so  to  speak,  crystallised.  But  it  is  just 
this  obvious,  flat  contradiction  that  makes  Groethe's  point 
of  view  in  1792  so  interesting  and  so  important.  At  this 
point  he  has  not  as  yet  developed  any  theory  of  his  own  ; 
there  is  nothing  under  discussion  but  a  few  easily-grasped 
facts,  as  to  the  correctness  of  which  both  parties  are  agreed, 
and  yet  both  hold  distinctly  opposite  views ;  neither 
of  them  even  understands  what  his  opponent  is  di'iving 
at.  On  the  one  side  are  a  number  of  physicists,  who, 
by  a  long  series  of  the  ablest  investigations,  the  most 
elaborate  calculations,  and  the  most  ingenious  inven- 
tions, have  brought  optics  to  such  perfection,  that  it, 
and  it  alone,  among  the  physical  sciences,  was  begin- 
ning almost  to  rival  astronomy  in  accui'acy.  Some  of 
them  have  made  the  phenomena  the  subject  of  direct  in- 
vestigation ;  all  of  them,  thanks  to  the  accuracy  with 
which  it  is  possible  to  calculate  beforehand  the  result 
of  every  variety  in  the  construction  and  combination  of 
instruments,  have  had  the  opportunity  of  putting  the 
inferences  deduced  from  Newton's  views  to  the  test  of 
experiment,  and  all,  without  exception,  agree  in  ac- 
cepting them.  On  the  other  side  is  a  man  whose 
remarkable  mental  endowments,  and  whose  singular 
talent  for  seeing  through  whatever  obscures  reality,  we 


ON  goethe's  scientific  reseahciie?.         45 

have  had  occasion  to  recognise,  not  only  in  poetry,  but 
also  in  the  descriptive  parts  of  the  natural  sciences ;  and 
this  man  assures  us  with  the  utmost  zeal  that  the  physicists 
are  wrong :  he  is  so  convinced  of  the  correctness  of  his  own 
view,  that  he  cannot  explain  the  contradiction  except  by 
assuming  narrowness  or  malice  on  their  part,  and  finally 
declares  that  he  cannot  help  looking  upon  his  own  achieve- 
ment in  the  theory  of  colour  as  far  more  valuable  than 
anything  he  has  accomplished  in  poetry.^ 

So  flat  a  contradiction  leads  us  to  suspect  that  there 
must  be  behind  some  deeper  antagonism  of  principle, 
some  difference  of  organisation  between  his  mind  and 
theirs,  to  prevent  them  from  understanding  each  other. 
I  will  try  to  indicate  in  the  following  pages  what  I  con- 
ceive to  be  the  grounds  of  this  antagonism. 

Goethe,  though  he  exercised  his  powers  in  many  spheres 
of  intellectual  activity,  is  nevertheless,  par  excellence^ 
a  poet.  Now  in  poetry,  as  in  every  other  art,  the  essen- 
tial thing  is  to  make  the  material  of  the  art,  be  it  words, 
or  music,  or  colour,  the  direct  vehicle  of  an  idea.  In  a 
perfect  work  of  art,  the  idea  must  be  present  and  domi- 
nate the  whole,  almost  unknown  to  the  poet  himself,  not 
as  the  result  of  a  long  intellectual  process,  but  as  inspired 
by  a  direct  intuition  of  the  inner  eye,  or  by  an  outbui'st  of 
excited  feeling. 

An  idea  thus  embodied  in  a  work  of  art,  and  dressed 
in  the  garb  of  reality,  does  indeed  make  a  vivid  im- 
pression by  appealing  directly  to  the  senses,  but  loses,  of 
course,  that  universality  and  that  intelligibility  which  it 
would  have  had  if  presented  in  the  form  of  an  abstract 
notion.  The  poet,  feeling  how  the  charm  of  his  works  is 
involved  in  an  intellectual  process  of  this  type,  seeks  to 
apply  it  to  other  materials.  Instead  of  trying  to  arrange 
the  phenomena  of  nature  under  definite  conceptions,  in- 
'  See  Eckermann's  Conversations. 


46         ON  Goethe's  scientific  kesearches. 

dependent  of  intuition,  he  sits  down  to  contemplate  them 
as  he  would  a  work  of  art,  complete  in  itself,  and  certain  to 
yield  up  its  central  idea,  sooner  or  later,  to  a  sufficiently 
susceptible  student.  Accordingly,  wh^n  he  sees  the  skull  on 
the  Lido,  which  suggests  to  him  the  vertebral  theory  of 
the  cranium,  he  remarks  that  it  serves  to  revive  his  old 
belief,  already  confirmed  by  experience,  that  Nature  has 
no  secrets  from  the  attentive  observer.  So  again  in  his 
first  conversation  with  Schiller  on  the  '  Metamorphosis  of 
Plants.'  To  Schiller,  as  a  follower  of  Kant,  the  idea  is 
the  goal,  ever  to  be  sought,  but  ever  unattainable,  and 
therefore  never  to  be  exhibited  as  realised  in  a  phenome- 
non. Goethe,  on  the  other  hand,  as  a  genuine  poet, 
conceives  that  he  finds  in  the  phenomenon  the  direct 
expression  of  the  idea.  He  himself  tells  us  that  nothing 
brought  out  more  sharply  the  separation  between  himself 
and  Schiller.  This,  too,  is  the  secret  of  his  affinity  with 
the  natural  philosophy  of  Schelling  and  Hegel,  which 
likewise  proceeds  from  the  assumption  that  Nature  shows 
us  by  direct  intuition  the  several  steps  by  which  a  con- 
ception is  developed.  Hence,  too,  the  ardour  with  which 
Hegel  and  his  school  defended  Goethe's  scientific  views. 
Moreover  this  view  of  Nature  accounts  for  the  war  which 
Goethe  continued  to  wage  against  complicated  experi- 
mental researches.  Just  as  a  genuine  work  of  art  cannot 
bear  retouching  by  a  strange  hand,  so  he  .would  have  us 
believe  Nature  resists  the  interference  of  the  experimenter 
who  tortures  her  and  disturbs  her ;  and  in  revenge,  mis- 
leads the  impertinent  kill-joy  by  a  distorted  image  of 
herself. 

Accordingly,  in  his  attack  upon  Newton  he  often 
sneers  at  spectra,  tortured  through  a  number  of  narrow 
slits  and  glasses,  and  commends  the  experiments  that  can 
be  made  in  the  open  air  under  a  bright  sun,  not  merely 
as  particularly  easy  and  particularly  enchanting,  but  also 


ON  Goethe's  scientific  reseakches.         47 

as  particularly  convincing  I  The  poetic  turn  of  mind  is 
very  marked  even  in  his  morphological  researches.  If 
we  only  examine  what  has  really  been  accomplished  by 
the  help  of  the  ideas  which  he  contributed  to  science, 
we  shall  be  struck  by  the  very  singular  relation  which 
they  bear  to  it.  No  one  will  refuse  to  be  convinced  if 
you  lay  before  him  the  series  of  transformations  by  which 
a  leaf  passes  into  a  stamen,  an  arm  into  a  fin  or  a  wing, 
a  vertebra  into  the  occipital  bone.  The  idea  that  all 
the  parts  of  a  flower  are  modified  leaves,  reveals  a  con- 
necting law,  which  surprises  us  into  acquiescence.  But 
now  try  and  define  the  leaf-like  organ,  determine  its 
essential  characteristics,  so  as  to  include  all  the  forms 
that  we  have  named.  You  will  find  yourself  in  a  difii- 
culty,  for  all  distinctive  marks  vanish,  and  you  have 
nothing  left,  except  that  a  leaf  in  the  wider  sense  of  the 
term  is  a  lateral  appendage  of  the  axis  of  a  plant.  Try 
then  to  express  the  proposition  '  the  parts  of  the  flower 
are  modified  leaves'  in  the  language  of  scientific  defi- 
nition, and  it  reads,  '  the  parts  of  the  flower  are  lateral 
appendages  of  the  axis.'  To  see  this  does  not  require  a 
Groethe.  So  again  it  has  been  objected,  and  not  unjustly, 
to  the  vertebral  theory,  that  it  must  extend  the  notion  of 
a  vertebra  so  much  that  nothing  is  left  but  the  bare  fact 
— a  vertebra  is  a  bone.  We  are  equally  perplexed  if  we 
try  to  express  in  clear  scientific  language  what  we  mean 
by  saying  that  such  and  such  a  part  of  one  animal 
corresponds  to  such  and  such  a  part  of  another.  We  do 
not  mean  that  their  physiological  use  is  the  same,  for  the 
same  piece  which  in  a  bird  serves  as  the  lower  jaw, 
becomes  in  mammals  a  tiny  tympanal  bone.  Nor  would 
the  shape,  the  position,  or  the  connection  of  the  part  in 
question  with  other  parts,  serve  to  identify  it  in  all  cases. 
But  yet  it  has  been  found  possible  in  most  cases,  by 
following  the  intermediate  steps,  to  determine  with  toler- 


48  ON   GOETHE'S   SCIENTIFIC  RESEARCHES, 

able  certainty  which  parts  correspond  to  each  other. 
Groethe  himself  said  this  very  clearly  :  he  says,  in  speaking 
of  the  vertebral  theory  of  the  skull,  '  Such  an  apergu, 
such  an  intuition,  conception,  representation,  notion,  idea, 
or  whatever  you  choose  to  call  it,  always  retains  some- 
thing esoteric  and  indefinable,  struggle  as  you  will 
against  it ;  as  a  general  principle,  it  may  be  enunciated, 
but  cannot  be  proved;  in  detail  it  may  be  exhibited, 
but  can  never  be  put  in  a  cut  and  dry  form.'  And  so,  or 
nearly  so,  the  problem  stands  to  this  day.  The  difference 
may  be  brought  out  still  more  clearly  if  we  consider 
how  physiology,  which  investigates  the  relations  of  vital 
processes  as  cause  and  effect,  would  have  to  treat  this 
idea  of  a  common  type  of  animal  structure.  The  science 
might  ask,  Is  it,  on  the  one  hand,  a  correct  view,  that 
during  the  geological  periods  that  have  passed  over  the 
earth,  one  species  has  been  developed  from  another,  so 
that,  for  example,  the  breast-fin  of  the  fish  has  gradually 
changed  into  an  arm  or  a  wing?  Or  again,  shall  we 
say  that  the  different  species  of  animals  were  created 
equally  perfect — that  the  points  of  resemblance  between 
them  are  to  be  ascribed  to  the  fact,  that  in  all  vertebrate 
animals  the  first  steps  in  development  from  the  egg  can 
only  be  effected  by  Nature  in  one  way,  almost  identical 
in  all  cases,  and  that  the  later  analogies  of  structure  are 
determined  by  these  features,  common  to  all  embryos  ? 
Probably  the  majority  of  observers  incline  to  the  latter 
view,^  for  the  agreement  between  the  embryos  of  dif- 
ferent vertebrate  animals,  in  the  earlier  stages,  is  very 
striking.  Thus  even  young  mammals  have  occasionally 
rudimentary  gills  on  the  side  of  the  neck,  like  fishes. 
It  seems,  in  fact,  that  what  are  in  the  mature  animals 
corresponding  parts,  originate  in  the  same  way  during 
the  process  of  development,  so  the  scientific  men  have 
'  This  was  written  before  the  appearance  of  Darwin's  OnV/tw  of  Specuie. 


ON  Goethe's  scientific  reseaeches.         49 

lately  begun  to  make  use  of  embryology  as  a  sort  of 
check  on  the  theoretical  views  of  comparative  anatomy. 
It  is  evident  that  by  the  application  of  the  physiological 
views  just  suggested,  the  idea  of  a  common  type  would 
acquire  definiteness  and  meaning  as  a  distinct  scientific 
conception.  Groethe  did  much :  he  saw  by  a  happy 
intuition  that  there  was  a  law,  and  he  followed  up  the 
indications  of  it  with  great  shrewdness.  But  what  law 
it  was,  he  did  not  see ;  nor  did  he  even  try  to  find  it  out. 
That  was  not  in  his  line.  Moreover,  even  in  the  present 
condition  of  science,  a  definite  view  on  the  question  is 
impossible  ;  the  very  form  in  which  it  should  be  proposed 
is  scarcely  yet  settled.  And  therefore  we  readily  admit 
that  in  this  department  Groethe  did  all  that  was  possible 
at  the  time  when  he  lived.  I  said  just  now  that  he 
treated  nature  like  a  work  of  art.  In  his  studies  on 
morphology,  he  reminds  one  of  a  spectator  at  a  play, 
with  strong  artistic  sympathies.  His  delicate  instinct 
makes  him  feel  how  all  the  details  fall  into  their  places, 
and  work  harmoniously  together,  and  how  some  common 
purpose  governs  the  whole ;  and  yet,  while  this  exquisite 
order  and  symmetry  give  him  intense  pleasure,  he  cannot 
formulate  the  dominant  idea.  That  is  reserved  for  the 
scientific  critic  of  the  drama,  while  the  artistic  spectator 
feels  perhaps,  as  Groethe  did  in  the  presence  of  natural 
phenomena,  an  antipathy  to  such  dissection,  fearing, 
though  without  reason,  that  his  pleasure  may  be  spoilt 
by  it. 

Goethe's  point  of  view  in  the  Theory  of  Colour  is  much 
the  same.  We  have  seen  that  he  rebels  against  the 
physical  theory  just  at  the  point  where  it  gives  complete 
and  consistent  explanations  from  principles  once  accepted. 
Evidently  it  is  not  the  insufficiency  of  the  theory  to 
explain  individual  cases  that  is  a  stumbling-block  to 
him.     He  takes  offence  at  the  assumption  made  for  the 


50         ox  Goethe's  scientific  researches. 

sake  of  explaining  the  phenomena,  which  seem  to  him  so 
absurd,  that  he  looks  upon  the  interpretation  as  no  inter- 
pretation at   all.     Above  all,  the  idea  that  white  light 
could  be  composed  of  coloured  light  seems  to  have  been 
quite  inconceivable  to  him  ;  at  the  very  beginning  of  the 
controversy,  he  rails  at  the  disgusting  Newtonian  white  of 
the  natural  philosophers,  an  expression  which  seems  to 
show  that  this  was  the  assumption  that  most  annoyed  him. 
Again,  in  his  later  attacks  on  Newton,  which  were  not 
published  till  after  bin  Theory  of  Colour  was  completed, 
he  rather  strives  to  show   that  Newton's  facts  might  be 
explained    on   his    own   hypothesis,    and    that   therefore 
Newton's  hypothesis  was  not  fully  proved,  than  attempts 
to  prove  that  hypothesis  inconsistent  with  itself  or  with 
the  facts.     Nay,  he  seems  to  consider  the  obviousness  of 
his  own  hypothesis  so  overwhelming,  that  it  need  only  be 
brought  forward  to  upset  Newton's  entirely.     There  are 
only  a  few  passages  where   he  disputes  the  experiments 
described  by  Newton.    Some  of  them,  apparently,  he  could 
not  succeed  in  refuting,  because  the  result  is  not  equally 
easy  to  observe  in  all  positions  of  the  lenses  used,  and 
because  he  was  unacquainted  with  the  geometrical  rela- 
tions by  which  the  most  favourable  positions  of  them  are 
determined.     In  other  experiments  on  the  separation  of 
simple  coloured  light  by  means  of  prisms  alone,  Groethe's 
objections  are  not  quite  groundless,  inasmuch  as  the  isola- 
tion of  single  colours  cannot  by  this  means  be  so  effectu- 
ally carried   out,  that  after  refraction  through   another 
prism  there  are  no  traces  of  other  tints  at  the  edges.     A 
complete  isolation  of  light  of  one   colour  can  only  be 
effected  by  very  carefully  arranged  apparatus,  consisting 
of  combined  prisms  and  lenses,  a  set  of  experiments  which 
Groethe  postponed  to  a  supplement,  and  finally  left  un- 
noticed.    When   he    complains    of  the    complication    of 
these  contrivances,  we  need  only  think  of  the  laborious 


ON  Goethe's  scientific  researches.         51 

and  roundabout  methods  which  chemists  must  often 
adopt  to  obtain  certain  elementary  bodies  in  a  pure  form ; 
and  we  need  not  be  surprised  to  find  that  it  is  impossible 
to  solve  a  similar  problem  in  the  case  of  light  in  the 
open  air  in  a  garden,  and  with  a  single  prism  in  one's 
hand.^  Goethe  must,  consistently  with  his  theory,  deny 
in  toto  the  possibility  of  isolating  pure  liglit  of  one  colour. 
Whether  he  ever  experimented  with  the  proper  apparatus 
to  solve  the  problem  remains  doubtful,  as  the  supplement 
in  which  he  promised  to  detail  these  experiments  was 
never  published. 

To  give  some  idea  of  the  passionate  way  in  which 
Goethe,  usually  so  temperate  and  even  courtier-like,  attacks 
Newton,  I  quote  from  a  few  pages  of  the  controversial 
part  of  his  work  the  following  expressions,  which  he  ap- 
plies to  the  propositions  of  this  consummate  thinker  in 
physical  and  astronomical  science  —  'incredibly  impu- 
dent;' '  mere  twaddle  ;'  '  ludicrous  explanation  ;'  'admi- 
rable for  school-children  in  a  go-cart ;'  '  but  I  see  nothing 
will  do  but  lying,  and  plenty  of  it.'  ^ 

Thus,  in  the  theory  of  colour,  Goethe  remains  faithful 
to  his  principle,  that  Nature  must  reveal  her  secrets  of  her 
own  free  will ;  that  she  is  but  the  transparent  representa- 
tion of  the  ideal  world.  Accordingly,  he  demands  as  a 
preliminary  to  the  investigation  of  physical  phenomena, 
that  the  observed  facts  shall  be  so  arranged  that  one  ex- 
plains the  other,  and  that  thus  we  may  attain  an  insight 

*  I  venture  to  add  that  I  am  acquainted  with  the  impossibility  of  decom- 
posing or  changing  simple  coloured  light,  the  two  principles  which  form 
the  basis  of  Newton's  theory,  not  merely  by  hearsay,  but  from  actual  obser- 
vation, having  been  under  the  necessity  in  one  of  my  own  researches  of 
obtaining  light  of  one  colour  in  a  state  of  the  greatest  possible  piirity.  (See 
Poggendorft's  Annalen,  vol.  Ixxxvi.  p.  50],  on  Sir  D.  Brewster's  Ntw  Analysis 
of  Svnlight.) 

2  Something  parallel  to  this  extraordinary  proceeding  of  Goethe's  may  be 
found  in  Hobbes's  attack  on  Wallis. — Tb. 


52         ox  Goethe's  scientific  eesearches. 

into  their  connection  without  ever  having  to  trust  to  any 
thing  but  our  senses.  This  demand  of  his  looks  most 
attractive,  but  is  essentially  wrong  in  principle.  For  a 
natural  phenomenon  is  not  considered  in  physical  science 
to  be  fully  explained  until  you  have  traced  it  back  to  the 
ultimate  forces  which  are  concerned  in  its  production  and 
its  maintenance.  Now,  as  we  can  never  become  cognizant 
of  forces  qua  forces,  but  only  of  their  effects,  we  are  com- 
pelled in  every  explanation  of  natural  phenomena  to 
leave  the  sphere  of  sense,  and  to  pass  to  things  which  are 
not  objects  of  sense,  and  are  defined  only  by  abstract  con- 
ceptions. When  we  find  a  stove  warm,  and  then  observe 
that  a  fire  is  burning  in  it,  we  say,  though  somewhat  in- 
accurately, that  the  former  sensation  is  explained  by  the 
latter.  But  in  reality  this  is  equivalent  to  saying,  we 
are  always  accustomed  to  find  heat  where  fire  is  burning ; 
now,  a  fire  is  burning  in  the  stove,  therefore  we  shall  find 
heat  there.  Accordingly  we  bring  our  single  fact  under 
a  more  general,  better  known  fact,  rest  satisfied  with  it, 
and  call  it  falsely  an  explanation.  Evidently,  however, 
the  generality  of  the  observation  does  not  necessarily  imply 
an  insight  into  causes  ;  such  an  insight  is  only  obtained 
when  we  can  make  out  what  forces  are  at  work  in  the 
fire,  and  how  the  effects  depend  upon  them. 

But  this  step  into  the  region  of  abstract  conceptions, 
which  must  necessarily  be  taken,  if  we  wish  to  penetrate 
to  the  causes  of  phenomena,  scares  the  poet  away.  In 
writing  a  poem  he  has  been  accustomed  to  look,  as  it 
were,  right  into  the  subject,  and  to  reproduce  his  intui- 
tion without  formulating  any  of  the  steps  that  led  him  to 
it.  And  his  success  is  proportionate  to  the  vividness  of 
the  intuition.  Such  is  the  fashion  in  which  he  would 
have  Nature  attacked.  But  the  natural  philosopher  in- 
sists on  transporting  him  into  a  world  of  invisible  atoms 
and  movements,  of  attractive  and  repulsive  forces,  whose 


ON   GOETHE'S   SCIENTIFIC  RESEAECHES.  58 

intricate  actions  and  reactions,  though  governed  by 
strict  laws,  can  scarcely  be  taken  in  at  a  glance.  To 
him  the  impressions  of  sense  are  not  an  irrefragable 
authority;  he  examines  what  claim  they  have  to  be 
trusted  ;  he  asks  whether  things  which  they  pronounce 
alike  are  really  alike,  and  whether  things  which  they 
pronounce  different  are  really  different ;  and  often  finds 
that  he  must  answer,  no  !  The  result  of  such  examination, 
as  at  present  understood,  is  that  the  organs  of  sense  do 
indeed  give  us  information  about  external  effects  pro- 
duced on  them,  but  convey  those  effects  to  our  conscious- 
ness in  a  totally  different  form,  so  that  the  character  of  a 
sensuous  perception  depends  not  so  much  on  the  proper- 
ties of  the  object  perceived  as  on  those  of  the  organ  by 
which  we  receive  the  information.  All  that  the  optic 
nerve  conveys  to  us,  it  conveys  under  the  form  of  a  sensa- 
tion of  light,  whether  it  be  the  rays  of  the  sun,  or  a  blow 
in  the  eye,  or  an  electric  current  passing  through  it. 
Again,  the  auditory  nerve  translates  everything  into  phe- 
nomena of  sound,  the  nerves  of  the  skin  into  sensations  of 
temperature  or  touch.  The  same  electric  current  whose 
existence  is  indicated  by  the  optic  nerve  as  a  flash  of 
light,  or  by  the  organ  of  taste  as  an  acid  flavour,  excites 
in  the  nerves  of  the  skin  the  sensation  of  burning.  The 
same  ray  of  sunshine,  which  is  called  light  when  it  falls 
on  the  eye,  we  call  heat  when  it  falls  on  the  skin.  But 
on  the  other  hand,  in  spite  of  their  different  effects  upon 
our  organisation,  the  daylight  wliich  enters  through  our 
windows,  and  the  heat  radiated  by  an  iron  stove,  do  not 
in  reality  differ  more  or  less  from  each  other  than  the 
red  and  blue  constituents  of  light.  In  fact,  just  as  in  the 
Undulatory  Theory,  the  red  rays  are  distinguished  from 
the  blue  rays  only  by  their  longer  period  of  vibration, 
and  their  smaller  refrangibility,  so  the  dark  heat  rays  of 
the  stove  have  a  still  longer  period  and  still  smaller  re- 


54  ON   GOETHE'S   SCIENTIFIC   EESEAECHES. 

frangibility  than  the  red  rays  of  light,  but  are  in  eveiy 
other  respect  exactly  similar  to  them.  All  these  rays, 
whether  luminous  or  non-luminous,  have  heating  proper- 
ties, but  only  a  certain  number  of  them,  to  which  for  that 
reason  we  give  the  name  of  light,  can  penetrate  through 
the  transparent  part  of  the  eye  to  the  optic  nerve,  and 
excite  a  sensation  of  light.  Perhaps  the  relation  between 
our  senses  and  the  external  world  may  be  best  enunciated 
as  follows :  our  sensations  are  for  us  only  symbols  of  the 
objects  of  the  external  world,  and  correspond  to  them 
only  in  some  such  way  as  written  characters  or  articulate 
words  to  the  things  they  denote.  They  give  us,  it  is  true, 
information  respecting  the  properties  of  things  without 
us,  but  no  better  information  than  we  give  a  blind  man 
about  colour  by  verbal  descriptions. 

We  see  that  science  has  arrived  at  an  estimate  of  the 
senses  very  different  from  that  which  was  present  to  the 
poet's  mind.  And  Newton's  assertion  that  white  was 
composed  of  all  the  colours  of  the  spectrum  was  the  first 
germ  of  the  scientific  view  which  has  subsequently  been 
developed.  For  at  that  time  there  were  none  of  those 
galvanic  observations  which  paved  the  way  to  a  know- 
ledge of  the  functions  of  the  nerves  in  the  production  of 
sensations.  Natural  philosophers  asserted  that  white,  to 
the  eye  the  simplest  and  purest  of  all  our  sensations  of 
colour,  was  compounded  of  less  pure  and  complex  mate- 
rials. It  seems  to  have  flashed  upon  the  poet's  mind  that 
all  his  principles  were  unsettled  by  the  results  of  this 
assertion,  and  that  is  why  the  hypothesis  seems  to  him  so 
unthinkable,  so  ineffably  absurd.  We  must  look  upon 
his  theory  of  colour  as  a  forlorn  hope,  as  a  desperate  at- 
tempt to  rescue  from  the  attacks  of  science  the  belief  in 
the  direct  truth  of  our  sensations.  And  this  will  account 
for  the  enthusiasm  with  which  he  strives  to  elaborate  and 
to  defend  his  theory,  for  the  passionate  irritability  with 


ON   GOETHE'S   SCIENTIFIC   RESEARCHES.  55 

which  he  attacks  his  opponent,  for  the  overweening  im- 
portance which  he  attaches  to  these  researches  in  com- 
parison with  his  other  achievements,  and  for  his  inacces- 
sibility to  conviction  or  compromise. 

If  we  now  turn  to  Groethe's  own  theories  on  the  subject, 
we  must,  on  the  grounds  above  stated,  expect  to  find  that 
he  cannot,  without  being  untrue  to  his  own  principle, 
give  us  anything  deserving  to  be  called  a  scientific  ex- 
planation of  the  phenomena,  and  that  is  exactly  what 
happens.  He  starts  with  the  proposition  that  all  colours 
are  darker  than  white,  that  they  have  something  of  shade 
in  them  (on  the  physical  theory,  white  compounded  of  all 
colours  must  necessarily  be  brighter  than  any  of  its 
constituents).  The  direct  mixture  of  dark  and  light,  of 
black  and  white,  gives  grey ;  the  colours  must  therefore 
owe  their  existence  to  some  form  of  the  co-operation  of 
light  and  shade.  Groethe  imagines  he  has  discovered 
it  in  the  phenomena  presented  by  slightly  opaque  or 
hazy  media.  Such  media  usually  look  blue  when  the 
light  falls  on  them,  and  they  are  seen  in  front  of  a  dark 
object,  but  yellow  when  a  bright  object  is  looked  at 
through  them.  Thus  in  the  day  time  the  air  looks  blue 
against  the  dark  background  of  the  sky,  and  the  sun, 
when  viewed,  as  is  the  case  at  sunset,  through  a  thick 
and  hazy  stratum  of  air,  appears  yellow.  The  physical 
explanation  of  this  phenomenon,  which,  however,  is  not 
exhibited  by  all  such  media,  as,  for  instance,  by  plates 
of  unpolished  glass,  would  lead  us  too  far  from  the  sub- 
ject. According  to  Goethe,  the  semi-opaque  medium 
imparls  to  the  light  something  corporeal,  something 
of  the  nature  of  shade,  such  as  is  requisite,  he  would 
say,  for  the  formation  of  colour.  This  conception  alone 
is  enough  to  perplex  anyone  who  looks  upon  it  as  a 
physical  explanation.  Does  he  mean  to  say  that  ma- 
terial particles  mingle  with  the  light  and  fly  away  with 


56         ON  Goethe's  scientific  eesearches. 

it  ?  But  this  is  Groethe's  fundamental  experiment,  this 
is  the  typical  phenomenon  under  which  he  tries  to  reduce 
all  the  phenomena  of  colour,  especially  tliose  connected 
with  the  prismatic  spectrum.  He  looks  upon  all  trans- 
parent bodies  as  slightly  hazy,  and  assumes  that  the 
prism  imparts  to  the  image  which  it  shows  to  an  observer 
something  of  its  own  opacity.  Here,  again,  it  is  hard  to 
get  a  definite  conception  of  what  is  meant.  Goethe 
seems  to  have  thought  that  a  prism  never  gives  per- 
fectly defined  images,  but  only  indistinct,  half-obliterated 
ones,  for  he  puts  them  all  in  the  same  class  with  the 
double  images  which  are  exhibited  by  parallel  plates  of 
glass  and  by  Iceland  spar.  The  images  formed  by  a 
prism  are,  it  is  true,  indistinct  in  compound  light,  but 
they  are  perfectly  defined  when  simple  light  is  used.  If 
you  examine,  he  says,  a  bright  surface  on  a  dark  ground 
through  a  prism,  the  image  is  displaced  and  blurred  by 
the  prism.  The  anterior  edge  is  pushed  forward  over  the 
dark  background,  and  consequently  a  hazy  light  on  a 
dark  ground  appears  blue,  while  the  other  edge  is  covered 
by  the  image  of  the  black  surface  which  comes  after  it, 
and,  consequently,  being  a  light  image  behind  a  hazy 
dark  colour,  appears  yellowish-red.  But  why  the  an- 
terior edge  appears  in  front  of  the  ground,  the  posterior 
edge  behind  it,  and  not  vice  versa,  he  does  not  explain. 
Let  us  analyse  this  explanation,  and  try  to  grasp  clearly 
the  conception  of  an  optical  image.  When  I  see  a 
bright  object  reflected  in  a  mirror,  the  reason  is  that 
the  light  which  proceeds  from  it  is  thrown  back  exactly 
as  if  it  came  from  an  object  of  the  same  kind  behind  the 
mirror.  The  eye  of  the  observer  receives  the  impression 
accordingly,  and  therefore  he  imagines  he  really  sees  the 
object.  Everyone  knows  there  is  nothing  real  behind 
the  mirror  to  correspond  to  the  image — that  no  light  can 
penetrate  thither,  but  that  what  is  called  the  image  is 


ON  goethe's  scientific  researches.         57 

simply  a  geometrical  point,  in  which  the  reflected  rays, 
if  produced  backwards,  would  intersect.  And,  accordingly, 
no  one  expects  the  image  to  produce  any  real  effect 
behind  the  mirror.  In  the  same  way  the  prism  shows 
us  images  of  objects  which  occupy  a  different  position 
from  the  objects  themselves  ;  that  is  to  say,  the  light 
which  an  object  sends  to  the  prism  is  refracted  by  it,  so 
that  it  appears  to  come  from  an  object  lying  to  one  side, 
called  the  image.  This  image,  again,  is  not  real ;  it  is,  as 
in  the  case  of  reflection,  the  geometrical  point  in  which 
the  refracted  rays  intersect  when  produced  backwards. 
And  yet,  according  to  G-oethe,  this  image  is  to  produce 
real  effects  by  its  displacement ;  the  displaced  patch  of 
light  makes,  he  says,  the  dark  space  behind  it  appear 
blue,  just  as  an  imperfectly  transparent  body  would,  and 
so  again  the  displaced  dark  patch  makes  the  bright  space 
behind  appear  reddish-yellow.  That  Goethe  really  treats 
the  image  as  an  actual  object  in  the  place  it  appears  to 
occupy  is  obvious  enough,  especially  as  he  is  compelled 
to  assume,  in  the  course  of  his  explanation,  that  the 
blue  and  red  edges  of  the  bright  space  are  respectively 
before  and  behind  the  dark  image  which,  like  it,  is 
displaced  by  the  prism.  He  does,  in  fact,  remain  loyal 
to  the  appearance  presented  to  the  senses,  and  treats  a 
geometrical  locus  as  if  it  were  a  material  object.  Again, 
he  does  not  scruple  at  one  time  to  make  red  and  blue 
destroy  each  other,  as,  for  example,  in  the  blue  edge  of  a 
red  surface  seen  through  the  prism,  and  at  another  to 
construct  out  of  them  a  beautiful  purple,  as  when  the 
blue  and  red  edges  of  two  neighbouring  white  surfaces 
meet  in  a  black  ground.  And  when  he  comes  to  Newton's 
more  complicated  experiments,  he  is  driven  to  still  more 
marvellous  expedients.  As  long  as  you  treat  his  explana- 
tions as  a  pictorial  way  of  representing  the  physical 
processes,  you  may  acquiesce  in  them,  and  even  frequently 


58         ON  Goethe's  scientific  researches. 

find  them  vivid  and  characteristic,  but  as  physical  eluci- 
dations of  the  phenomena  they  are  absolutely  irrational. 

In  conclusion,  it  must  be  obvious  to  everyone  that  the 
theoretical  part  of  the  Theory  of  Colour  is  not  natural 
philosophy  at  all ;  at  the  same  time  we  can,  to  a  certain 
extent,  see  that  the  poet  wanted  to  introduce  a  totally 
different  method  into  the  study  of  Nature,  and  more  or 
less  understand  how  he  came  to  do  so.  Poetry  is  con- 
cerned solely  with  the  '  beautiful  show '  which  makes  it 
possible  to  contemplate  the  ideal ;  how  that  show  is 
produced  is  a  matter  of  indifference.  Even  Nature  is,  in 
the  poet's  eyes,  but  the  sensible  expression  of  the  spiritual. 
The  natural  philosopher,  on  the  other  hand,  tries  to 
discover  the  levers,  the  cords,  and  the  pulleys,  which 
work  behind  the  scenes,  and  shift  them.  Of  course  the 
sight  of  the  machinery  spoils  the  beautiful  show,  and 
therefore  the  poet  would  gladly  talk  it  out  of  existence, 
and  ignoring  cords  and  pulleys  as  the  chimeras  of  a 
pedant's  brain,  he  would  have  us  believe  that  the  scenes 
shift  themselves,  or  are  governed  by  the  idea  of  the 
drama.  And  it  is  just  characteristic  of  Groethe,  that  he, 
and  he  alone  among  poets,  must  needs  break  a  lance 
with  natural  philosophers.  Other  poets  are  either  so 
entirely  carried  away  by  the  fire  of  their  enthusiasm  that 
they  do  not  trouble  themselves  about  the  disturbing 
influences  of  the  outer  world,  or  else  they  rejoice  in  tha 
triumphs  of  mind  over  matter,  even  on  that  unpropitious 
battlefield.  But  G-oethe,  whom  no  intensity  of  subjective 
feeling  could  blind  to  the  realities  around  him,  cannot 
rest  satisfied  until  he  has  stamped  reality  itself  with  the 
image  and  superscription  of  poetry.  This  constitutes 
the  peculiar  beauty  of  his  poetry,  and  at  the  same  time 
fully  accounts  for  his  resolute  hostility  to  the  machinery 
that  every  moment  threatens  to  disturb  his  poetic  repose, 
and  for  his  determination  to  attack  the  enemy  in  his  own 
camp. 


ON  goethe's  scientific  reseaeches.         59 

But  we  cannot  triumpli  over  the  machinery  of  matter 
by  ignoring  it ;  we  can  triumph  over  it  only  by  subordi- 
nating it  to  the  aims  of  our  moral  intelligence.  We  must 
familiarise  ourselves  with  its  levers  and  pulleys,  fatal 
though  it  be  to  poetic  contemplation,  in  order  to  be  able 
to  govern  them  after  our  own  will,  and  therein  lies  the 
complete  justification  of  physical  investigation,  and  its 
vast  importance  for  the  advance  of  human  civilisation. 

From  what  I  have  said  it  will  be  apparent  that 
Groethe  did  follow  the  same  line  of  thought  in  all  his 
contributions  to  science,  but  that  the  problems  he  en- 
countered were  of  diametrically  opposite  characters.  And, 
perhaps,  when  it  is  understood  how  the  self-same  cha- 
racteristic of  his  intellect,  which  in  one  branch  of  science 
won  for  him  immortal  renown,  entailed  upon  him  egre- 
gious failure  in  the  other,  it  will  tend  to  dissipate,  in  the 
minds  of  many  worshippers  of  the  great  poet,  a  lingering 
prejudice  against  natural  philosophers,  whom  they  sus- 
pect of  being  blinded  by  narrow  professional  pride  to  the 
loftiest  inspirations  of  genius. 
4 


ON  THE 

PHYSIOLOGICAL  CAUSES  OF  HARMONY 
IN  MUSIC. 

A  LECTURE  DELIVERED   IN   BONN   DURING   THE  WINTER  OP  1857. 


Ladies  and  GtENTLEMEN, — In  the  native  town  of  Beet- 
hoven, the  mightiest  among  the  heroes  of  harmony,  no 
subject  seemed  to  me  better  adapted  for  a  popular 
audience  thau  music  itself.  Following,  therefore,  the 
direction  of  my  researches  during  the  last  few  years,  I 
will  endeavour  to  explain  to  you  what  physics  and  physio- 
logy have  to  say  regarding  the  most  cherished  art  of  the 
Ehenish  land — music  and  musical  relations.  Music  has 
hitherto  withdrawn  itself  from  scientific  treatment  more 
than  any  other  art.  Poetry,  painting,  and  sculpture 
borrow  at  least  the  material  for  their  delineations  from 
the  world  of  experience.  They  portray  nature  and  man. 
Not  only  can  their  material  be  critically  investigated  in 
respect  to  its  correctness  and  truth  to  nature,  but  scien- 
tific art-criticism,  however  much  enthusiasts  may  have 
disputed  its  right  to  do  so,  has  actually  succeeded  in 
making  some  progress  in  investigating  the  causes  of  that 
aesthetic  pleasure  which  it  is  the  intention  of  these  arts  to 
excite.     In  music,  on  the  other  hand,  it  seems  at  first 


62  ON  THE   PHYSIOLOGICAL   CAUSES   OF 

sight  as  if  those  were  still  in  the  right  who  reject  all 
'  anatomisation  of  pleasurable  sensations.'  This  art,  bor- 
rowing no  part  of  its  material  from  the  experience  of  our 
senses  ;  not  attempting  to  describe,  and  only  exceptionally 
to  imitate  the  outer  world,  necessarily  withdi'aws  from 
scientific  consideration  the  chief  points  of  attack  which 
other  arts  present,  and  hence  seems  to  be  as  incompre- 
hensible and  wonderful  as  it  is  certainly  powerful  in  its 
effects.  We  are,  therefore,  obliged,  and  we  purpose,  to 
confine  ourselves,  in  the  first  place,  to  a  consideration  of 
the  material  of  the  art,  musical  sounds  or  sensations.  It 
always  struck  me  as  a  wonderful  and  peculiarly  inte- 
resting mystery,  that  in  the  theory  of  musical  sounds,  in 
the  physical  and  technical  foundations  of  music,  which 
above  all  other  arts  seems  in  its  action  on  the  mind  as 
the  most  immaterial,  evanescent,  and  tender  creator  of 
incalculable  and  indescribable  states  of  consciousness, 
that  here  in  especial  the  science  of  purest  and  strictest 
thought — mathematics — should  prove  preeminently  fer- 
tile. Thorough  bass  is  a  kind  of  applied  mathematics. 
In  considering  musical  intervals,  divisions  of  time,  and 
so  forth,  numerical  fractions,  and  sometimes  even  loga- 
rithms, play  a  prominent  part.  Mathematics  and  music  ! 
the  most  glaring  possible  opposites  of  human  thought ! 
and  yet  connected,  mutually  sustained  !  It  is  as  if  they 
would  demonstrate  the  hidden  consensus  of  all  the  actions 
of  our  mind,  which  in  the  revelations  of  genius  makes  us 
forefeel  unconscious  utterances  of  a  mysteriously  active 
intelligence. 

When  I  considered  physical  acoustics  from  a  physiolo- 
gical point  of  view,  and  thus  more  closely  followed  up 
the  part  which  the  ear  plays  in  the  perception  of  musical 
sounds,  much  became  clear  of  which  the  connection  had 
not  been  previously  evident.  I  will  attempt  to  inspire 
you  with  some  of  the  interest  which  these  questions  have 


HARMONY   IN   MUSIC.  63 

awakened  in  my  own  mind,  by  endeavouring  to  exhibit 
a  few  of  the  results  of  physical  and  physiological 
acoustics. 

The  short  space  of  time  at  my  disposal  obliges  me  to  con- 
fine my  attention  to  one  particular  point ;  but  I  shall  select 
the  most  important  of  all,  which  will  best  show  you  the 
significance  and  results  of  scientific  investigation  in  this 
field ;  I  mean  the  foundation  of  concord.  It  is  an  acknow- 
ledged fact  that  the  numbers  of  the  vibrations  of  concor- 
dant tones  bear  to  each  other  ratios  expressible  by  small 
whole  numbers.  But  why  ?  What  have  the  ratios  of 
small  whole  numbers  to  do  with  concord  ?  This  is  an  old 
riddle,  propounded  by  Pythagoras,  and  hitherto  unsolved. 
Let  us  see  whether  the  means  at  the  command  of  modern 
science  will  furnish  the  answer. 

First  of  all,  what  is  a  musical  tone  ?  Common  expe- 
rience teaches  us  that  all  sounding  bodies  are  in  a  state 
of  vibration.  This  vibration  can  be  seen  and  felt ;  and 
in  the  case  of  loud  sounds  we  feel  the  trembling  of  the 
air  even  without  touching  the  sounding  bodies.  Physical 
science  has  ascertained  that  any  series  of  impulses  which 
produce  a  vibration  of  the  air  will,  if  repeated  with  sufii- 
cient  rapidity,  generate  sound. 

This  sound  becomes  a  musical  tone,  when  such  rapid 
impulses  recur  with  perfect  regularity  and  in  precisely 
equal  times.  Irregular  agitation  of  the  air  generates  only 
noise.  The  'pitch  of  a  musical  tone  depends  on  the 
number  of  impulses  which  take  place  in  a  given  time  ; 
the  more  there  are  in  the  same  time  the  higher  or  sharper 
is  the  tone.  And,  as  before  remarked,  there  is  found  to  be 
a  close  relationship  between  the  well-known  harmonious 
musical  intervals  and  the  number  of  the  vibrations  of  the 
air.  If  twice  as  many  vibrations  are  performed  in  the 
same  time  for  one  tone  as  for  another,  the  first  is  the 
octave  above  the  second.     If  the  numbers  of  vibrations 


64  0]^  THE   PHYSIOLOGICAL   CAUSES   OF 

in  the  same  time  are  as  2  to  3,  the  two  tones  form  a  fifth  ; 
if  they  are  as  4  to  5,  the  two  tones  form  a  major  third. 

If  you  observe  that  the  numbers  of  the  vibrations  which 
generate  the  tones  of  the  major  chord  C  E  Gr  c  are  in  the 
ratio  of  the  numbers  4:5:6:8,  you  can  deduce  from 
these  all  other  relations  of  musical  tones,  by  imagining 
a  new  major  chord,  having  the  same  relations  of  the  num- 
bers of  vibrations,  to  be  formed  upon  each  of  the  above- 
named  tones.  The  numbers  of  vibrations  within  the 
limits  of  audible  tones  which  would  be  obtained  by 
executing  the  calculation  thus  indicated,  are  extraordi- 
narily different.  Since  the  octave  above  any  tone  has 
twice  as  many  vibrations  as  the  tone  itself,  the  second 
octave  above  will  have  four  times,  the  third  has  eight 
times  as  many.  Our  modem  pianofortes  have  seven 
octaves.  Their  highest  tones,  therefore,  perform  128 
vibrations  in  the  time  that  their  lowest  tone  makes  one 
single  vibration. 

The  deepest  C,  which  our  pianos  usually  possess,  answers 
to  the  sixteen-foot  open  pipe  of  the  organ — musicians  call 
it  the  '  contra-C ' — and  makes  thirty-three  vibrations  in 
one  second  of  time.  This  is  very  nearly  the  limit  of  audi- 
bility. You  will  have  observed  that  these  tones  have  a 
dull,  bad  quality  of  sound  on  the  piano,  and  that  it  is 
difficult  to  determine  their  pitch  and  the  accuracy  of  their 
tuning.  On  the  organ  the  contra-C  is  somewhat  more 
powerful  than  on  the  piano,  but  even  here  some  uncer- 
tainty is  felt  in  judging  of  its  pitch.  On  larger  organs 
there  is  a  whole  octave  of  tones  below  the  contra-C, 
reaching  to  the  next  lower  C,  with  16^  vibrations  in  a 
second.  But  the  ear  can  scarcely  separate  these  tones 
from  an  obscure  drone  ;  and  the  deeper  they  are  the  more 
plainly  can  it  distinguish  the  separate  impulses  of  the  air 
to  which  they  are  due.  Hence  they  are  used  solely  in  con- 
junction with  the  next  higher  octaves,  to  strengthen  their 
notes,  and  produce  an  impression  of  greater  depth. 


HAEMONY   IN  MUSIC.  65 

With  the  exception  of  the  organ,  all  musical  instru- 
ments, however  diverse  the  methods  in  which  their  sounds 
are  produced,  have  their  limit  of  depth  at  about  the  same 
point  in  the  scale  as  the  piano ;  not  because  it  would  be 
impossible  to  produce  slower  impulses  of  the  air  of  suffi- 
cient power,  but  because  the  ear  refuses  its  office,  and 
hears  slower  impulses  separately,  without  gathering  them 
up  into  single  tones. 

The  often  repeated  assertion  of  the  French  physicist 
Savart,  that  he  heard  tones  of  eight  vibrations  in  a 
second,  upon  a  peculiarly  constructed  instrument,  seems 
due  to  an  error. 

Ascending  the  scale  from  the  contra-C,  pianofortes 
usually  have  a  compass  of  seven  octaves,  up  to  the  so- 
called  five-accented  c,  which  has  4,224  vibrations  in  a 
second.  Among  orchestral  instruments  it  is  only  the 
piccolo  flute  which  can  reach  as  high,  and  this  will  give 
even  one  tone  higher.  The  violin  usually  mounts  no 
higher  than  the  e  below,  which  has  2,640  vibrations — of 
course  we  except  the  gymnastics  of  heaven-scaling  virtuosi, 
who  are  ever  striving  to  excruciate  their  audience  by 
some  new  impossibility.  Such  performers  may  aspire 
to  three  whole  octaves  lying  above  the  five-accented  c, 
and  very  painful  to  the  ear,  for  their  existence  has  been 
established  by  Despretz,  who,  by  exciting  small  tuning- 
forks  with  a  violin  bow,  obtained  and  heard  the  eight- 
accented  c,  having  32,770  vibrations  in  a  second.  Here 
the  sensation  of  tone  seemed  to  have  reached  its  upper 
limit,  and  the  intervals  were  really  undistinguishable  in 
the  later  octaves. 

The  musical  pitch  of  a  tone  depends  entirely  on  the 
number  cf  vibrations  of  the  air  in  a  second,  and  not  at 
all  upon  the  mode  in  which  they  are  produced.  It  is 
quite  indifferent  whether  they  are  generated  by  the 
vibrating  strings  of  a  piano  or  violin,  the  vocal  chords  of 


6Q  ON  THE   PHYSIOLOGICAL   CAUSES   OF 

the  human  larynx,  the  metal  tongues  of  the  harmonium, 
the  reeds  of  the  clarionet,  oboe  and  bassoon,  the  trembling 
lips  of  the  trumpeter,  or  the  air  cut  by  a  sharp  edge  in 
organ  pipes  and  flutes. 

A  tone  of  the  same  number  of  vibrations  has  always 
the  same  pitch,  by  whichever  one  of  these  instruments  it 
is  produced.  That  which  distinguishes  the  note  A  of  a 
piano  for  example,  from  the  equally  high  A  of  the  violin, 
flute,  clarionet,  or  trumpet,  is  called  the  quality  of  the 
tone,  and  to  this  we  shall  have  to  recur  presently. 

As  an  interesting  example  of  these  assertions,  I  beg  to  show 
you  a  peculiar  physical  instrument  for  producing  musical  tones, 
called  the  siren,  Fig.  1,  which  is  especially  adapted  to  establish 
the  properties  resulting  from  the  ratios  of  the  numbers  of  vibra- 
tions. 

In  order  to  produce  tones  upon  this  instrument,  the  portventg 
go  and  gi  are  connected  by  means  of  flexible  tubes  with  a 
bellows.  The  air  enters  into  round  brass  boxes,  ao  and  aj,  and 
escapes  by  the  perforated  covers  of  these  boxes  at  Cq  and  Cj.  But 
the  holes  for  the  escape  of  air  are  not  perfectly  free.  Immediately 
before  the  covers  of  both  boxes  there  are  two  other  perforated 
discs,  fastened  to  a  perpendicular  axis  k,  which  turns  with  great 
readiness.  In  the  figure,  only  the  perforated  disc  can  be  seen  at 
Cq,  and  immediately  below  it  is  the  similarly  perforated  cover  of 
the  box.  In  the  upper  box,  c,,  only  the  edge  of  the  disc  is 
visible.  If  then  the  holes  of  the  disc  are  precisely  opposite  to 
those  of  the  cover,  the  air  can  escape  freely.  But  if  the  disc  is 
made  to  revolve,  so  that  some  of  its  unperforated  portions  stand 
before  the  holes  of  the  box,  the  air  cannot  escape  at  all.  On 
turning  the  disc  rapidly,  the  vent-holes  of  the  box  are  alternately 
opened  and  closed.  During  the  opening,  air  escapes;  during 
the  closure,  no  air  can  pass.  Hence  the  continuous  stream  of 
air  from  the  bellows  is  converted  into  a  series  of  discontinuous 
puffs,  which,  when  they  follow  one  another  with  suflicient 
rapidity,  gather  themselves  together  into  a  tone. 

Each  of  the  revolving  discs  of  this  instrument  (which  is  more 
complicated  in  its  construction  than  any  one  of  the  kind  hitherto 
made,  and  hence  admits  of  a  much  greater  number  of  combina- 


HAHMONY  IN  MUSIC. 


67 


Fia.  I. 


68  ox   THE   PHYSIOLOGICAL   CAUSES   OF 

tions  of  tone)  has  fo^l^  concentric  circles  of  holes,  the  lower  set 
having  8,  10,  12,  18,  and  the  upper  set  9,  12,  15,  and  16,  holes 
respectively.  The  series  of  holes  in  the  covers  of  the  boxes  are 
precisely  the  same  as  those  in  the  discs,  but  under  each  of  them 
lies  a  perforated  ring,  which  can  be  so  arranged,  by  means  of  the 
stops  i  i  i  i,  that  the  corresponding  holes  of  the  cover  can  either 
communicate  freely  Avith  the  inside  of  the  box,  or  are  entirely 
cut  off  from  it.  We  are  thus  enabled  to  use  any  one  of  the 
eight  series  of  holes  singly,  or  combined  two  and  two,  or  three 
and  three  together,  in  any  arbitrary  manner. 

The  round  boxes,  hg  h^  and  hj  h,,  of  which  halves  only  are 
drawn  in  the  figure,  serve  by  their  resonance  to  soften  the  harsh- 
ness of  the  tone. 

The  holes  in  the  boxes  and  discs  are  cut  obliquely,  so  that 
when  the  air  enters  the  boxes  through  one  or  more  of  the  series 
of  holes,  the  wind  itself  drives  the  discs  round  with  a  per- 
petually increasing  velocity. 

On  beginning  to  blow  the  instrument,  we  first  hear  separate 
impulses  of  the  air,  escaping  as  puffs,  as  often  as  the  holes  of 
the  disc  pass  in  front  of  those  of  the  box.  These  puffs  of  air 
follow  one  another  more  and  more  quickly,  as  the  velocity  of 
the  revolving  discs  increases,  just  like  the  puffs  of  steam  of  a 
locomotive  on  beginning  to  move  with  the  train.  They  next 
produce  a  whirring  and  whizzing,  Avhich  constantly  becomes 
more  rapid.  At  last  we  hear  a  dull  drone,  which,  as  the 
velocity  further  increases,  gradually  gains  in  pitch  and  strength. 

Suppose  that  the  discs  have  been  brought  to  a  velocity  of 
33  revolutions  in  a  second,  and  that  the  series  Avith  8  holes  has 
been  opened.  At  each  revolution  of  the  disc  all  these  8  holes 
will  pass  before  each  separate  hole  of  the  cover.  Hence  there 
will  be  8  puffs  for  each  revolution  of  the  disc,  or  8  times  33, 
that  is,  264  puffs  in  a  second.  This  gives  us  the  once-accented  c' 
of  our  musical  scale,  [that  is  '  middle  c,'  written  on  the  leger  line 
between  the  bass  and  treble  staves.]  But  on  opening  the  series 
of  16  holes  instead,  we  have  twice  as  many,  or  16  times  33, 
that  is,  528  vibrations  in  a  second.  We  hear  exactly  the  octave 
above  the  first  c',  that  is  the  twice-accented  c",  [or  c  on  the  third 
space  of  the  treble  staff.]  By  opening  both  the  series  of  8  and 
16  holes  at  once,  we  have  both  c'  and  c"  at  once,  and  can  con- 
vince ourselves  that  we  have  the  absolutely  pure  concord  of  the 


HAEMOxYY  IN   MUSIC.  69 

octave.  By  taking  8  and  12  holes,  -which  give  numbers  of 
vibrations  in  the  ratio  of  2  to  3,  we  have  the  concord  of  a 
perfect  fifth.  Similarly  12  and  16  or  9  and  12  give  fourths, 
12  and  15  give  a  major  third,  and  so  on. 

The  upper  box  is  furnished  with  a  contrivance  for  slightly 
sharpening  or  flattening  the  tones  which  it  produces.  This  box 
is  movable  upon  an  axis,  and  connected  with  a  toothed  wheel, 
which  is  worked  by  the  driver  attached  to  the  handle  d.  By 
turning  the  handle  slowly  while  one  of  the  series  of  holes  in  the 
upper  box  is  in  use,  the  tone  will  be  sharper  or  flatter,  according 
as  the  box  moves  in  the  opposite  direction  to  the  disc,  or  in  the 
same  direction  as  the  disc.  When  the  motion  is  in  the  opposite 
direction,  the  holes  meet  those  of  the  disc  a  little  sooner  than 
they  otherwise  would,  the  time  of  vibration  of  the  tone  is 
shortened,  and  the  tone  becomes  sharper.  The  contrary  ensues 
in  the  other  case. 

Now,  on  blowing  through  8  holes  below  and  16  above,  we 
have  a  perfect  octave,  as  long  as  the  upper  box  is  still ;  but 
when  it  is  in  motion,  the  pitch  of  the  upper  tone  is  slightly 
altered,  and  the  octave  becomes  false. 

On  blowing  through  12  holes  above  and  18  below,  the  result 
is  a  perfect  fifth  as  long  as  the  upper  box  is  at  rest,  but  if  it 
moves  the  concord  is  perceptibly  injured. 

These  experiments  with  the  siren  show  us,  therefore  : — 

1.  That  a  series  of  puffs  following  one  another  with  sufficient 
rapidity,  produce  a  musical  tone. 

2.  That  the  more  rapidly  they  follow  one  another,  the  sharper 
is  the  tone. 

3.  That  when  the  ratio  of  the  number  of  vibrations  is  exactly 
1  to  2,  the  result  is  a  perfect  octave ;  when  it  is  2  to  3,  a 
perfect  fifth  ;  when  it  is  3  to  4,  a  pure  fourth,  and  so  on.  The 
slightest  alteration  in  these  ratios  destroys  the  purity  of  the 
concord- 

You  will  perceive,  from  what  has  been  hitherto  ad- 
duced, that  the  human  ear  is  affected  by  vibrations  of  the 
air,  within  certain  degrees  of  rapidity — viz.  from  about 
20  to  about  32,000  in  a  second — and  that  the  sensation 
of  musical  tone  arises  from  this  affection. 


70  ON   THE   PHYSIOLOGICAL   CAUSES   OF 

That  the  sensation  thus  excited  is  a  sensation  of  musical 
tone,  does  not  depend  in  any  way  upon  the  peculiar 
manner  in  which  the  air  is  agitated,  but  solely  on  the 
peculiar  powers  of  sensation  possessed  by  our  ears  and 
auditory  nerves.  I  remarked,  a  little  while  ago,  that 
when  the  tones  are  loud  the  agitation  of  the  air  is  per- 
ceptible to  the  skin.  In  this  way  deaf  mutes  can  perceive 
the  motion  of  the  air,  which  we  call  sound.  But  they  do 
not  hear,  that  is,  they  have  no  sensation  of  tone  in  the 
ear.  They  feel  the  motion  by  the  nerves  of  the  skin, 
producing  that  peculiar  description  of  sensation  called 
whirring.  The  limits  of  the  rapidity  of  vibration  within 
winch  the  ear  feels  an  agitation  of  the  air  to  be  sound, 
depend  also  wholly  upon  the  peculiar  constitution  of  the 
ear. 

When  the  siren  is  turned  slowly,  and  hence  the  puffs  of 
air  succeed  each  other  slowly,  you  hear  no  musical  sound. 
By  the  continually  increasing  rapidity  of  its  revolution, 
no  essential  change  is  produced  in  the  kind  of  vibration 
of  the  air.  Nothing  new  happens  externally  to  the  ear. 
The  only  new  result  is  the  sensation  experienced  by  the 
ear,  which  then  for  the  first  time  begins  to  be  affected  by 
the  agitation  of  the  air.  Hence  the  more  rapid  vibrations 
receive  a  new  name,  and  are  called  Sound  If  you  admire 
paradoxes,  you  may  say  that  aerial  vibrations  do  not  be- 
come sound  until  they  fall  upon  a  hearing  ear. 

I  must  now  describe  the  propagation  of  sound  through 
the  atmosphere.  The  motion  of  a  mass  of  air  through 
which  a  tone  passes,  belongs  to  the  so-called  wave  motions 
• — a  class  of  motions  of  great  importance  in  physics. 
Light,  as  well  as  sound,  is  one  of  these  motions. 

The  name  is  derived  from  the  analogy  of  waves  on  the 
surface  of  water,  and  these  will  best  illustrate  the  pecu- 
liarity of  this  description  of  motion. 

AYhen  a  point  in  a  surface  of  still  water  is  agitated — as 


HAEMONY   IN   MUSIC.  71 

by  throwing  in  a  stone — the  motion  thus  caused  is  pro- 
pagated in  the  form  of  waves,  which  spread  in  rings  over 
the  surface  of  the  water.  The  circles  of  waves  continue 
to  increase  even  after  rest  has  been  restored  at  the  point 
first  affected.  At  the  same  time  the  waves  become  con- 
tinually lower,  the  further  they  are  removed  from  the 
centre  of  motion,  and  gradually  disappear.  On  each 
wave-ring  we  distinguish  ridges  or  crests,  and  hollows  or 
troughs. 

Crest  and  trough  together  form  a  wave,  and  we  measure 
its  length  from  one  crest  to  the  next. 

While  the  wave  passes  over  the  surface  of  the  fluid,  the 
particles  of  the  water  which  form  it  do  not  move  on  with 
it.  This  is  easily  seen,  by  floating  a  chip  of  straw  on  the 
water.  When  the  waves  reach  the  chip,  they  raise  or 
depress  it,  but  when  they  have  passed  over  it,  the  position 
of  the  chip  is  not  perceptibly  changed. 

Now  a  light  floating  chip  has  no  motion  different  from 
that  of  the  adjacent  particles  of  water.  Hence  we  con- 
clude that  these  particles  do  not  follow  the  wave,  but, 
after  some  pitching  up  and  down,  remain  in  their  original 
position.  That  which  really  advances  as  a  wave  is,  con- 
sequently, not  the  particles  of  water  themselves,  but  only 
a  superficial  form,  which  continues  to  be  built  up  by  fresh 
particles  of  water.  The  paths  of  the  separate  particles  of 
water  are  more  nearly  vertical  circles,  in  which  they  re- 
volve with  a  tolerably  uniform  velocity,  as  long  as  the 
waves  pass  over  them. 

In  Fig.  2  the  dark  wave-line,  ABC,  represents  a  section  of 
the  surface  of  the  water,  over  which  waves  are  running  in  the 
direction  of  the  arrows  above  a  and  c.  The  three  circles,  a,  b, 
and  c,  represent  the  paths  of  particular  particles  of  water  at  the 
surface  of  the  wave.  The  particle  which  revolves  in  the  circle  b, 
is  supposed  at  the  time  that  the  surface  of  the  water  presents  the 
form  A  B  C,  to   be  at  its  highest  point  B,  and  the  particles  re- 


IZ  ox   THE   PHYSIOLOGICAL   CAUSES    OF 

volving  in  the  circles  a  and  c  to  be  simultaneously  in  their  lowest 
positions. 

The  respective  particles  of  water  revolve  in  these  circles  in 
the  direction  marked  by  the  arrows.  The  dotted  curves  repre- 
sent other  positions  of  the  passing  waves,  at  equal  intervals  of 
time,  partly  before  the  assumption  of  the  ABC  position  (as  for 
the  crests  between  a  and  b),  and  partly  after  the  same  (for  tha 
crests  between  b  and  c).  The  positions  of  the  crests  are  marked 
with  figures.  The  same  figures  in  the  three  circles,  show  where 
the  respective  revolving  particle  would  be,  at  the  moment  the 
wave  assumed  the  corresponding  form.  It  will  be  noticed  that 
the  particles  advance  by  equal  arcs  of  the  circles,  as  the  crest  of 
the  wave  advances  by  equal  distances  parallel  to  the  water  leveL 

In  the  circle  b  it  will  be  further  seen,  that  the  particle  ol 
water  in  its  positions  1,  2,  3,  hastens  to  meet  the  approaching 


Fig.  2. 


■wave-crests.  1,  2,  3,  rises  on  its  left  hand  side,  is  then  carried  on 
by  the  crest  from  4  to  7  in  the  direction  of  its  advance,  after- 
wards halts  behind  it,  sinks  down  again  on  the  right  side,  and 
finally  reaches  its  original  position  at  13.  (In  the  Lecture  itself,  • 
Fig.  2  was  replaced  by  a  Avorking  model,  in  which  the  movable 
particles,  connected  by  threads,  really  revolved  in  circles,  while 
connecting  elastic  threads  represented  the  surface  of  the  water.) 

All  particles  at  the  surface  of  the  water,  as  you  see  by  this 
drawing,  describe  equal  circles.  The  particles  of  water  at  dif- 
ferent depths  move  in  the  same  way,  but  as  the  deptlis  increase, 
the  diameters  of  their  circles  of  revolution  rapidly  diminish. 

In  this  way,  then,  arises  the  appearance  of  a  progressive  motion 
along  the  surface  of  the  water,  while  in  reality  the  moving  par- 
ticles of  water  do  not  advance  with  the  wave,  but  perpetually 
revolve  in  their  small  circular  orbits. 


HARMONY   IN   MUSIC.  73 

To  return  from  waves  of  water  to  waves  of  sound. 
Imagine  an  elastic  fluid  like  air  to  replace  the  water,  and 
the  waves  of  this  replaced  water  to  be  compressed  b}^  an 
inflexible  plate  laid  on  their  surface,  the  fluid  being  pre- 
vented from  escaping  laterally  from  the  pressure.  Then 
on  the  waves  being  thus  flattened  out,  the  ridges  where 
the  fluid  had  been  heaped  up  will  produce  much  greater 
density  than  the  hollows,  from  which  the  fluid  had  been 
removed  to  form  the  ridges.  Hence  the  ridges  are  re- 
placed by  condensed  strata  of  air,  and  the  hollows  by 
rarefied  strata.  Now  further  imagine  that  these  com- 
pressed waves  are  propagated  by  the  same  law  as  before, 
and  that  also  the  vertical  circular  orbits  of  the  several 
particles  of  water  are  compressed  into  horizontal  straight 
lines.  Then  the  waves  of  sound  will  retain  the  peculiarity 
of  having  the  particles  of  air  only  oscillating  backwards 
and  forwards  in  a  straight  line,  while  the  wave  itself 
remains  merely  a  progressive  form  of  motion,  continually 
composed  of  fresh  particles  of  air.  The  immediate  result 
then  would  be  waves  of  sound  spreading  out  horizontally 
from  their  origin. 

But  the  expansion  of  waves  of  sound  is  not  limited, 
like  those  of  water,  to  a  horizontal  surface.  They  can 
spread  out  in  any  direction  whatsoever.  Suppose  the  circles 
generated  by  a  stone  thrown  into  the  water  to  extend  in 
all  directions  of  space,  and  you  will  have  the  spherical 
waves  of  air  by  which  sound  is  propagated. 

Hence  we  can  continue  to  illustrate  the  peculiarities  of 
the  motion  of  sound,  by  the  well-known  visible  motions 
of  waves  of  water. 

The  length  of  a  wave  of  water,  measured  from  crest  to 
crest,  is  extremely  different.  A  falling  drop,  or  a  breath 
of  air,  gently  curls  the  surface  of  the  water.  The  waves 
in  the  wake  of  a  steamboat  toss  the  swimmer  or  skiff 
severely.     But  the  waves  of  a  stormy  ocean  can  find  room 


74  ON   THE   PHYSIOLOGICAL   CAUSES   OF 

in  their  hollows  for  the  keel  of  a  ship  of  the  line,  and 
their  ridges  can  scarcely  be  overlooked  from  the  mast- 
head. The  waves  of  sound  present  similar  differences. 
The  little  curls  of  water  with  short  lengths  of  wave  corre- 
spond to  high  tones,  the  giant  ocean  billows  to  deep  tones. 
Thus  the  contrabass  C  has  a  wave  thirty-five  feet  long,  its 
higher  octave  a  wave  of  half  the  length,  while  the  highest 
tones  of  a  piano  have  waves  of  only  three  inches  in  length.^ 
You  perceive  that  the  pitch  of  the  tone  corresponds 
to  the  length  of  the  wave.  To  this  we  should  add  that 
the  height  of  the  ridges,  or,  transferred  to  air,  the  degree 
of  alternate  condensation  and  rarefaction,  corresponds  to 
the  loudness  and  intensity  of  the  tone.  But  waves  of  the 
same  height  may  have  different  forms.  The  crest  of 
the  ridge,  for  example,  may  be  rounded  off  or  pointed. 
Corresponding  varieties  also  occur  in  waves  of  sound  of 
the  same  pitch  and  loudness.  The  so-called  tinihre  or 
quality  of  tone  is  what  corresponds  to  the  fovin  of  the 
waves  of  water.  The  conception  of  form  is  transferred 
from  waves  of  water  to  waves  of  sound.  Supposing  waves 
of  water  of  different  forms  to  be  pressed  flat  as  before,  the 
surface,  having  been  levelled,  will  of  course  display  no 
differences  of  form,  but,  in  the  interior  of  the  mass  of 
water,  we  shall  have  different  distributions  of  pressure, 
and  hence  of  density,  which  exactly  correspond  to  the 
differences  of  form  in  the  still  uncompressed  surface.  In 
this  sense  then  we  can  continue  to  speak  of  the  form  of 
waves  of  sound,  and  can  represent  it  geometrically.  We 
make  the  curve  rise  where  the  pressure,  and  hence  density, 
increases,  and  fall  where  it  diminishes — just  as  if  we  had 

'  The  exact  lengths  of  waves  corresponding  to  certain  iwtcs,  or  symbols 
of  tone,  depend  upon  the  standard  pitch  assigned  to  one  particular  note, 
and  this  differs  in  different  countries.  Hence  the  figures  of  the  author 
have  been  left  unreduced.  They  are  sufficiently  near  to  those  usually 
adopted  in  England,  to  occasion  no  difficulty  to  the  reader  in  these  general 
remarks. — Te. 


HARMONY   IN   MUSIC.  75 

a  compressed  fluid  beneath  the  curve,  which  would  expand 
to  the  height  of  the  curve  in  order  to  regain  its  natural 
density. 

Unfortunately,  the  form  of  waves  of  sound,  on  which 
depends  the  quality  of  the  tones  produced  by  various 
sounding  bodies,  can  at  present  be  assigned  in  only  a  very 
few  cases. 

Amons:  the  forms  of  waves  of  sound  which  we  are  able 
to  determine  with  more  exactness,  is  one  of  great  im- 
portance, here  termed  the  simple  or  pure  wave-form,  and 
represented  in  Fig.  3. 

Fig.  3. 


It  can  be  seen  in  waves  of  water  only  when  their  height 
is  small  in  comparison  with  their  length,  and  they  run 
over  a  smooth  surface  without  external  disturbance,  or 
without  any  action  of  wind.  Eidge  and  hollow  are  gently 
rounded  off,  equally  broad  and  symmetrical,  so  that,  if  ^7e 
inverted  the  curve,  the  ridges  would  exactly  fit  into  the 
hollows,  and  conversely.  This  form  of  wave  would  be 
more  precisely  defined  by  saying  that  the  particles  of 
water  describe  exactly  circular  orbits  of  small  diameters, 
with  exactly  uniform  velocities.  To  this  simple  wave- 
form corresponds  a  peculiar  species  of  tone,  which,  from 
reasons  to  be  hereafter  assigned,  depending  upon  its  rela- 
tion to  quality,  we  will  term  a  simple  tone.  Such  tones 
are  produced  by  striking  a  tuning-fork,  and  holding  it 
before  the  opening  of  a  properly-tuned  resonance  tube. 
The  tone  of  tuneful  human  voices,  singing  the  vowel  oo 
in  too,  in  the  middle  positions  of  their  register,  appears 
not  to  differ  materially  from  this  form  of  wave. 

We  also  know  the  laws  of  the  motion  of  strings  with 


76 


ox   THE   PHYSIOLOGICAL   CAUSES   OP 


sufficient  accuracy  to  assign  in  some  cases  the  form  of 
motion  which  they  impart  to  the  air.  Thus  Fig.  4  repre- 
sents the  forms  successively  assumed  by  a  string  struck, 
as  in  the  German  Zither^  by  a  pointed  style,  [the  plectrum 


Fig.  4. 


of  the  ancient  lyra,  or  the  quill  of  the  old  harpsichord, 
which  may  be  easily  imitated  on  a  guitar].  A  a  represents 
the  form  assumed  by  the  string  at  the  moment  of  percus- 
sion. Then,  at  equal  intervals  of  time,  follow  the  forms 
B,  C,  D,  E,  F,  G- ;  and  then  in  inverse  order,  F,  E,  D,  C, 
B,  A,  and  so  on  in  perpetual  repetition.  The  form  of 
motion  which  such  a  string,  by  means  of  an  attached  sound- 
ing board,  imparts  to  the  surrounding  air,  probably  corre- 
sponds to  the  broken  line  in  Fig.  5,  where  h  h  indicates 
the  position  of  equilibrium,  and  the  letters  a  b  c  d  e  f  g 
show  the  line  of  the  wave  which  is  produced  by  the  action 


HAEMOTsT  IN  MUSIC.  77 

of  several  forms  of  string  marked  by  the  corresponding 
capital  letters  in  Fig.  4.  It  is  easily  seen  how  greatly 
this  form  of  Avave  (which  of  course  could  not  occur  in 


Tig.  5. 


^-!L 


o   e    g    e    c 


r^— r^ 


water)  differs  from  that  of  Fig.  3  (independently  of  mag- 
nitude), as  the  string  only  imparts  to  the  air  a  series  of 
short  impulses,  alternately  directed  to  opposite  sides.^ 

The  waves  of  air  produced  by  the  tone  of  a  violin 
would,  on  the  same  principle,  be  represented  by  Fig.  6. 

Fia.  6. 


During  each  period  of  vibration  the  pressure  increases 
uniformly,  and  at  the  end  falls  back  suddenly  to  its 
minimum. 

It  is  to  such  differences  in  the  forms  of  the  waves  of 
sound  that  the  variety  of  quality  in  musical  tones  is  due. 
We  may  even  carry  the  analogy  further.  The  more  uni- 
formly rounded  the  form  of  wave,  the  softer  and  milder  is 
the  quality  of  tone.  The  more  jerking  and  angular  the 
wave-form,  the  more  piercing  the  quality.  Tuning-forks, 
with  their  rounded  forms  of  wave  (Fig.  3),  have  an  extra- 
ordinarily soft  quality;  and  the  qualities  of  tone  generated 
by  the  zither  and  violin  resemble  in  harshness  the  angu- 
larity of  their  wave-forms.     (Figs.  5  and  6.) 

'  It  is  here  assumed  that  the  soimding-board  and  air  in  contact  with  it 
immediately  obey  the  impulse  given  by  the  end  of  the  string  without 
exercising  a  perceptible  reaction  on  the  motion  of  the  string. 


78  ox   THE   PHYSIOLOGICAL   CAUSES    OF 

Finally,  I  would  direct  your  attention  to  an  instructive 
spectacle,  which  I  have  never  been  able  to  view  without  a 
certain  degree  of  physico-scientific  delight,  because  it  dis- 
plays to  the  bodily  eye,  on  the  surface  of  water,  what 
otherwise  could  only  be  recognised  by  the  mind's  eye  of 
the  mathematical  thinker  in  a  mass  of  air  traversed  in  all 
directions  by  waves  of  sound.  I  allude  to  the  composition 
of  many  different  systems  of  waves,  as  they  pass  over  one 
another,  each  undisturbedly  pursuing  its  own  path.  We 
can  watch  it  from  the  parapet  of  any  bridge  spanning  a 
river,  but  it  is  most  complete  and  sublime  when  viewed 
from  a  cliff  beside  the  sea.  It  is  then  rare  not  to  see 
innumerable  systems  of  waves,  of  various  length,  propa- 
gated in  various  directions.  The  longest  come  from  the 
deep  sea  and  dash  against  the  shore.  Where  the  boiling 
breakers  burst  shorter  waves  arise,  and  run  back  again 
towards  the  sea.  Perhaps  a  bird  of  prey  darting  after  a 
fish  gives  rise  to  a  system  of  circular  waves,  which, 
rocking  over  the  undulating  surface,  are  propagated  with 
the  same  regularity  as  on  the  mirror  of  an  inland  lake. 
And  thus,  from  the  distant  horizon,  where  white  lines  of 
foam  on  the  steel-blue  surface  betray  the  coming  trains  of 
wave,  down  to  the  sand  beneath  our  feet,  where  the  im- 
pression of  their  arcs  remains,  there  is  unfolded  before  our 
eyes  a  sublime  image  of  immeasurable  power  and  unceasing- 
variety,  which,  as  the  eye  at  once  recognises  its  pervading 
order  and  law,  enchains  and  exalts  without  confusing  the 
mind. 

Now,  just  in  the  same  way  you  must  conceive  the  air 
of  a  concert-hall  or  ballroom  traversed  in  every  direction, 
and  not  merely  on  the  surface,  by  a  variegated  crowd  of 
intersecting  wave-systems.  From  the  mouths  of  the  male 
singers  proceed  waves  of  six  to  twelve  feet  in  length ; 
from  the  lips  of  the  songstresses  dart  shorter  waves,  from 
eighteen  to  thirty-six  inches  long.     The  rustling  of  silken 


HAEMONY   IN   MUSIC.  79 

skirts  excites  little  curls  in  the  air,  each  instrument  in 
the  orchestra  emits  its  peculiar  waves,  and  all  these  sys- 
tems expand  spherically  from  their  respective  centres,  dart 
through  each  other,  are  reflected  from  the  walls  of  the 
room,  and  thus  rush  backwards  and  forwards,  until  they 
succumb  to  the  greater  force  of  newly  generated  tones. 

Although  this  spectacle  is  veiled  from  the  material  eye, 
we  have  another  bodily  organ,  the  ear,  specially  adapted  to 
reveal  it  to  us.  This  analyses  the  interdigitation  of  the 
waves,  which  in  such  cases  would  be  far  more  confused 
than  the  intersection  of  the  water  undulations,  separates 
the  several  tones  which  compose  it,  and  distinguishes  the 
voices  of  men  and  women — nay,  even  of  individuals — the 
peculiar  qualities  of  tone  given  out  by  each  instrument, 
the  rustling  of  the  dresses,  the  footfalls  of  the  walkers, 
and  so  on. 

It  is  necessary  to  examine  the  circumstances  with  greater 
minuteness.  When  a  bird  of  prey  dips  into  the  sea,  rings 
of  waves  arise,  which  are  propagated  as  slowly  and  regu- 
larly upon  the  moving  surface  as  upon  a  surface  at  rest. 
These  rings  are  cut  into  the  curved  surface  of  the  waves 
in  precisely  the  same  way  as  they  would  have  been  into 
the  still  surface  of  a  lake.  The  form  of  the  external  sur- 
face of  the  water  is  determined  in  this,  as  in  other  more 
complicated  cases,  by  taking  the  height  of  each  point  to 
be  the  height  of  all  the  ridges  of  the  waves  which  coin- 
cide at  this  point  at  one  time,  after  deducting  the  sum 
of  all  similarly  simultaneously  coincident  hollows.  Such 
a  sum  of  positive  magnitudes  (the  ridges)  and  negative 
magnitudes  (the  hollows),  where  the  latter  have  to  be 
subtracted  instead  of  being  added,  is  called  an  alge- 
braical sum.  Using  this  term,  then,  we  may  say  that 
the  height  of  every  point  of  the  surface  of  the  water  is 
equal  to  the  algebraical  sum  of  all  the  jportions  of  the 
waves  which  at  that  moment  there  concur. 


80  ox   THE   PHYSIOLOGICAL   CAUSES   OF 

It  is  the  same  with  the  waves  of  sound.  They,  too,  are 
added  together  at  every  point  of  the  mass  of  air,  as  well 
as  in  contact  with  the  listener's  ear.  For  them  also  the 
degree  of  condensation  and  the  velocity  of  the  particles  of 
air  in  the  passages  of  the  organ  of  hearing  are  equal  to  the 
algebraical  sums  of  the  separate  degrees  of  condensation 
and  of  the  velocities  of  the  waves  of  sound,  considered 
apart.  This  single  motion  of  the  air  produced  by  the 
simultaneous  action  of  various  sounding  bodies,  has  now 
to  be  analysed  by  the  ear  into  the  separate  parts  which 
correspond  to  their  separate  effects.  For  doing  this  the 
ear  is  much  more  unfavourably  situated  than  the  eye. 
The  latter  surveys  the  whole  undulating  surface  at  a 
glance.  But  the  ear  can,  of  course,  only  perceive  the 
motion  of  the  particles  of  air  which  impinge  upon  it. 
And  yet  the  ear  solves  its  problem  with  the  greatest 
exactness,  certainty,  and  determinacy.  This  power  of  the 
ear  is  of  supreme  importance  for  hearing.  Were  it  not 
present  it  would  be  impossible  to  distinguish  different 
tones. 

Some  recent  anatomical  discoveries  appear  to  give  a 
clue  to  the  explanation  of  this  important  power  of  the 
ear. 

You  will  all  have  observed  the  phenomena  of  the  sym- 
pathetic production  of  tones  in  musical  instruments,  espe- 
cially stringed  instruments.  The  string  of  a  pianoforte 
when  the  damper  is  raised  begins  to  vibrate  as  soon  as  its 
proper  tone  is  produced  in  its  neighbourhood  with  suffi- 
cient force  by  some  other  means.  When  this  foreign  tone 
ceases  the  tone  of  the  string  will  be  heard  to  continue 
some  little  time  longer.  If  we  put  little  paper  riders  on 
the  string  they  will  be  jerked  off  when  its  tone  is  thus 
produced  in  the  neighbourhood.  This  sympathetic  action 
of  the  string  depends  on  the  impact  of  the  vibrating 
particles  of  air  against  the  string  and  its  sounding-board. 


HARMONY   IN  MUSIC.  81 

Each  separate  wave-crest  (or  condensation)  of  air  which 
passes  by  the  string  is,  of  course,  too  weak  to  produce  a  sen- 
sible motion  in  it.  But  when  a  long  series  of  wave-crests 
(or  condensations)  strike  the  string  in  such  a  manner  that 
each  succeeding  one  increases  the  slight  tremour  which 
resulted  from  the  action  of  its  predecessors,  the  effect 
finally  becomes  sensible.  It  is  a  process  of  exactly  the 
same  nature  as  the  swinging  of  a  heavy  bell.  A  powerful 
man  can  scarcely  move  it  sensibly  by  a  single  impulse.  A 
boy,  by  pulling  the  rope  at  regular  intervals  corresponding 
to  the  time  of  its  oscillations,  can  gradually  bring  it  into 
violent  motion. 

This  peculiar  reinforcement  of  vibration  depends  entirely 
on  the  rhythmical  application  of  the  impulse.  When  the 
bell  has  been  once  made  to  vibrate  as  a  pendulum  in  a 
very  small  arc,  and  the  boy  always  pulls  the  rope  as  it 
falls,  and  at  a  time  that  his  pull  augments  the  existing 
velocity  of  the  bell,  this  velocity,  increasing  slightly  at 
each  pull,  will  gradually  become  considerable.  But  if 
the  boy  apply  his  power  at  irregular  intervals,  sometimes 
increasing  and  sometimes  diminishing  the  motion  of  the 
bell,  he  will  produce  no  sensible  effect. 

In  the  same  way  that  a  mere  boy  is  thus  enabled  to 
swing  a  heavy  bell,  the  tremours  of  light  and  mobile  air 
suffice  to  set  in  motion  the  heavy  and  solid  mass  of  steel 
contained  in  a  tuning-fork,  provided  that  the  tone  which 
is  excited  in  the  air  is  exactly  in  unison  with  that  of  the 
fork,  because  in  this  case  also  every  impact  of  a  wave  of 
air  against  the  fork  increases  the  motions  excited  by  the 
like  previous  blows. 

This  experiment  is  most  conveniently  performed  on  a 
fork.  Fig.  7,  which  is  fastened  to  a  sounding-board,  the 
air  being  excited  by  a  similar  fork  of  precisely  the  same 
pitch.  If  one  is  struck,  the  other  will  be  found  after  a 
few  seconds  to  be  sounding  also.     Then  damp  the  first 


82 


ox   THE   PHYSIOLOGICAL   CAUSES    OF 


fork,  by  touching  it  for  a  moment  with  a  finger,  and  the 
second  will  continue  the  tone.  The  second  will  then 
bring  the  first  into  vibration,  and  so  on. 

But  if  a  very  small  piece  of  wax  be  attached  to  the 
ends  of  one  of  the  forks,  whereby  its  pitch  will  be 
rendered  scarcely  perceptibly  lower  than  the  other,  the 
sympathetic  vibration  of  the  second  fork  ceases,  because 
the  times  of  oscillation  are  no  longer  the  same  in  each. 
The  blows  which  the  waves  of  air  excited  by  the  first 
inflict  upon  the  sounding  board  of  the  second  fork,  are 
indeed  for  a  time  in  the  same  direction  as  the  motions  of 

Fio.  7. 


the  second  fork,  and  consequently  increase  the  latter, 
but  after  a  very  short  time  they  cease  to  be  so,  and 
consequently  destroy  the  slight  motion  which  they  had 
previously  excited. 

Lighter  and  more  mobile  elastic  bodies,  as  for  example 
strings,  can  be  set  in  motion  by  a  much  smaller  number 
of  aerial  impulses.  Hence  they  can  be  set  in  sympathetic 
motion  much  more  easily  than  tuning  forks,  and  by 
means  of  a  musical  tone  which  is  far  less  accurately  in 
unison  with  themselves. 


HARMONY   IN  MUSIC.  83 

Now,  then,  if  several  tones  are  sounded  in  the  neigh- 
bourhood of  a  pianoforte,  no  string  can  be  set  in  sym- 
pathetic vibration  unless  it  is  in  unison  with  one  of  those 
tones.  For  example,  depress  the  forte  pedal  (thus  raising 
the  dampers),  and  put  paper  riders  on  all  the  strings. 
They  will  of  course  leap  off  when  their  strings  are  put  in 
vibration.  Then  let  several  voices  or  instruments  sound 
tones  in  the  neighbourhood.  All  those  riders,  and  only 
those,  will  leap  off  which  are  placed  upon  strings  that 
correspond  to  tones  of  the  same  pitch  as  those  sounded. 
You  perceive  that  a  pianoforte  is  also  capable  of  analysing 
the  wave  confusion  of  the  air  into  its  elementary  con- 
stituents. 

The  process  which  actually  goes  on  in  our  ear  is 
probably  very  like  that  just  described.  Deep  in  the 
petrous  bone  out  of  which  the  internal  ear  is  hollowed, 
lies  a  peculiar  organ,  the  cochlea  or  snail  shell — a  cavity 
filled  with  water,  and  so  called  from  its  resembLance  to 
the  shell  of  a  common  garden  snail.  This  spiral  passage 
is  divided  throughout  its  length  into  three  sections, 
upper,  middle,  and  lower,  by  two  membranes  stretched 
in  the  middle  of  its  height.  The  Marchese  Corti  dis- 
covered some  very  remarkable  formations  in  the  middle 
section.  They  consist  of  innumerable  plates,  micro- 
scopically small,  and  arranged  orderly  side  by  side,  like 
the  keys  of  a  piano.  They  are  connected  at  one  end  with 
the  fibres  of  the  auditory  nerve,  and  at  the  other  with 
the  stretched  membrane. 

Fig.  8  shows  this  extraordinarily  complicated  arrange- 
ment for  a  small  part  of  the  partition  of  the  cochlea.  The 
arches  which  leave  the  membrane  at  d  and  are  re-inserted 
at  e,  reaching  their  greatest  height  between  m  and  o, 
are  probably  the  parts  which  are  suited  for  vibration. 
They  are  spun  round  with  innumerable  fibrils,  among 
which  some  nerve  fibres  can  be  recognised,  coming  to 
5 


84 


OK  THE   PHYSIOLOGICAL   CiiUSES   OF 


them  througli  the  holes  near  c.  The  transverse  fibres 
g,  h,  i,  k,  and  the  cells  o,  also  appear  to  belong  to  the 
nervous  system.  There  are  about  three  thousand  arches 
similar  to  d  e,  lying  orderly  beside  each  other,  like  the 
keys  of  a  piano  in  the  whole  length  of  the  partition  of 
the  cochlea. 


In  the  so-called  vestibulum,  also,  where  the  nerves 
expand  upon  little  membranous  bags  swimming  in  water, 
elastic  appendages,  similar  to  stiff  hairs,  have  been  lately 
discovered  at  the  ends  of  the  nerves.  The  anatomical 
arrangement   of   these   appendages   leaves    scarcely   any 


HAEMONY   IN   MUSIC.  85 

room  to  doubt  that  they  are  set  into  sympathetic  vibra- 
tion by  the  waves  of  sound  which  are  conducted  through 
the  ear.  Now  if  we  venture  to  conjecture — it  is  at 
present  only  a  conjecture,  but  after  careful  consideration 
I  am  led  to  think  it  very  probable — that  every  such 
appendage  is  tuned  to  a  certain  tone  like  the  strings 
of  a  piano,  then  the  recent  experiment  with  a  piano 
shows  you  that  when  (and  only  when)  that  tone  is 
sounded  the  corresponding  hair-like  appendage  may  vibrate, 
and  the  corresponding  nerve-fibre  experience  a  sensa- 
tion, so  that  the  presence  of  each  single  such  tone  in  the 
midst  of  a  whole  confusion  of  tones  must  be  indicated 
by  the  corresponding  sensation. 

Experience  then  shows  us  that  the  ear  really  possesses 
the  power  of  analysing  waves  of  air  into  their  elementary 
forms. 

By  compound  motions  of  the  air,  we  have  hitherto 
meant  such  as  have  been  caused  by  the  simultaneous 
vibration  of  several  elastic  bodies.  Now,  since  the  forms 
of  the  waves  of  sound  of  dififerent  musical  instruments 
are  dififerent,  there  is  room  to  suppose  that  the  kind  of 
vibration  excited  in  the  passages  of  the  ear  by  one  such 
tone  will  be  exactly  the  same  as  the  kind  of  vibration 
which  in  another  case  is  there  excited  by  two  or  more 
instruments  sounded  together.  If  the  ear  analyses  the 
motion  into  its  elements  in  the  latter  case,  it  cannot  well 
avoid  doing  so  in  the  former,  where  the  tone  is  due  to  a 
single  source.     And  this  is  found  to  be  really  the  case. 

I  have  previously  mentioned  the  form  of  wave  with 
gently  rounded  crests  and  hollows,  and  termed  it  simple  or 
pure  (p.  75).  In  reference  to  this  form  the  French  mathe- 
matician Fourier  has  established  a  celebrated  and  impor- 
tant theorem  which  may  be  translated  from  mathematical 
into  ordinary  language  thus :  Any  form  of  wave  what- 
ever can  he  compounded  of  a  number  of  simple  waves  of 


86 


ON  THE   PHYSIOLOGICAL   CAUSES   OF 


different  lengths.  The  longest  of  these  simple  waves 
has  the  same  length  as  that  of  the  given  form  of  wave, 
the  others  have  lengths  one-half,  one-third,  one-fourth,  &c. 
as  great. 

By  the  different  modes  of  uniting  the  crests  and 
hollows  of  these  simple  waves,  an  endless  multiplicity  of 
wave-forms  may  be  produced. 

For   example,  the  wave-curves  A  and  B,  Fig.  9,  represent 
Fig.  9. 

.^4 


waves  of  simple  tones,  B  making  twice  as  many  vibrations  as  A  in 
a  second  of  time,  and  being  consequently  an  octave  higher  in  pitch. 
C  and  D,  on  the  other  hand,  represent  the  waves  which  result 
from  the  superposition  of  B  on  A.  The  dotted  curves  in  the 
first  halves  of  C  and  D  are  repetitions  of  so  much  of  the  figure  A. 
In  C,  the  initial  point  e  of  the  curve  B  coincides  with  the  initial 
point  do  of  A.  But  in  D,  the  deepest  point  bg  of  the  first  hollow 
in  B  is  placed  under  the  initial  point  of  A.  The  result  is  two 
different  compound-curves,  the  first  C  having  steeply  ascending 


HAEMONY   m  MUSIC. 


87 


and  more  gently  descending  crests,  but  so  related  that,  by  re- 
versing the  figure,  the  elevations  would  exactly  fit  into  the 
depressions.  But  in  D  we  have  pointed  crests  and  flattened 
hollows,  which  are,  however,  symmetrical  with  respect  to  right 
and  left. 

Other  forms  are  shown  in  Fig.  10,  which  are  also  compounded 
of  two  simple  waves,  A  and  B,  of  which  B  makes  three  times  as 
many  vibrations  in  a   second  as  A,  and   consequently  is   the 

FiQ.  10. 


twelfth  higher  in  pitch.  The  dotted  curves  in  C  and  D  are,  as 
before,  repetitions  of  A.  C  has  flat  crests  and  flat  hollows,  D 
has  pointed  crests  and  pointed  hollows. 

These  extremely  simple  examples  will  suflice  to  give  a  con- 
ception of  the  great  multiplicity  of  forms  resulting  from  this 
method  of  composition.  Supposing  that  instead  of  two,  several 
simple  waves  were  selected,  with  heights  and  initial  points 
arbitrarily   chosen,   an    endless  variety   of   changes    could   be 


88  ox   THE   PHYSIOLOGICAL   CAUSES   OF 

effected,  and,  in  point  of  fact,  any  given  form  of  wave  could  be 
reproduced.^ 

When  various  simple  waves  concur  on  the  surface  of 
water,  the  compound  wave-form  has  only  a  momentary 
existence,  because  the  longer  waves  move  faster  than  the 
shorter,  and  consequently  the  two  kinds  of  wave  imme- 
diately separate,  giving  the  eye  an  opportunity  of  recog- 
nising the  presence  of  several  systems  of  waves.  But 
when  waves  of  sound  are  similarly  compounded,  they 
never  separate  again,  because  long  and  short  waves  traverse 
air  with  the  same  velocity.  Hence  the  compound  wave 
is  permanent,  and  continues  its  course  unchanged,  so  that 
when  it  strikes  the  ear,  there  is  nothing  to  indicate 
whether  it  originally  left  a  musical  instrument  in  this 
form,  or  whether  it  had  been  compounded  on  the  way, 
out  of  two  or  more  undulations. 

Now  what  does  the  ear  do  ?  Does  it  analyse  this 
compound  wave?  Or  does  it  grasp  it  as  a  whole?  The 
answer  to  these  questions  depends  upon  the  sense  in 
which  we  take  them.  \ye  must  distinguish  two  different 
points— the  audible  sensation,  as  it  is  developed  with- 
out any  intellectual  interference,  and  the  conception, 
which  we  form  in  consequence  of  that  sensation.  We 
have,  as  it  were,  to  distinguish  between  the  material  ear 
of  the  body  and  the  spiritual  ear  of  the  mind.  The 
material  ear  does  precisely  what  the  mathematician 
effects  by  means  of  Fourier's  theorem,  and  what  the 
pianoforte  accomplishes  when  a  confused  mass  of  tones  is 
presented  to  it.  It  analyses  those  wave-forms  which  were 
not  originally  due  to  simple  undulations,  such  as  those 
furnished  by  tuning  forks,  into  a  sum  of  simple  tones,  and 

>  Of  course  the  waves  could  not  overhang,  but  waves  of  such  a  form 
would  have  no  possible  analogue  in  waves  of  sound  [which  the  reader  will 
recollect  are  not  actually  in  the  forms  here  drawn,  but  have  only  condensa- 
tions and  rarefactions,  conveniently  replaced  by  these  forms,  p.  73]. 


HARMOiinr  m  anisic.  89 

feels  the  tone  due  to  each  separate  simple  wave  sepa- 
rately, whether  the  compound  wave  originally  proceeded 
from  a  source  capable  of  generating  it,  or  became  com- 
pounded on  tlie  way. 

For  example,  on  striking  a  string,  it  will  give  a  tone  corre- 
sponding, as  we  have  seen,  to  a  wave-form  widely  different  from 
that  of  a  simple  tone.  When  the  ear  analyses  this  wave-form 
into  a  sum  of  simple  waves,  it  hears  at  the  same  time  a  series  of 
simple  tones  corresponding  to  these  waves. 

Strings  are  peculiarly  favourable  for  such  an  investigation, 
because  they  are  themselves  capable  of  assuming  extremely  dif- 
ferent forms  in  the  course  of  their  vibration,  and  these  forms 
may  also  be  considered,  like  those  of  aerial  undulations,  as  com- 
pounded of  simple  waves.  Fig.  4,  p.  76,  shows  the  consecutive 
forms  of  a  string  struck  by  a  simple  rod.  Fig,  11,  p.  90,  gives  a 
number  of  other  forms  of  vibration  of  a  string,  corresponding  to 
simple  tones.  The  continuous  line  shows  the  extreme  displace- 
ment of  the  string  in  one  direction,  and  the  dotted  line  in  the  other. 
At  a  the  string  produces  its  fundamental  tone,  the  deepest  simple 
tone  it  can  produce,  vibrating  in  its  whole  length,  first  on  one 
side  and  then  on  the  other.  At  b  it  falls  into  two  vibrating 
sections,  separated  by  a  single  stationary  point  /3,  called  a  node 
(knot).  The  tone  is  an  octave  higher,  the  same  as  each  of  the 
two  sections  would  separately  produce,  and  it  performs  twice  as 
many  vibrations  in  a  second  as  tlie  fundamental  tone.  At  c  we 
have  two  nodes,  yj  and  yg?  ^^^  three  vibrating  sections,  each 
vibrating  three  times  as  fast  as  the  fundamental  tone  and  hence 
giving  its  twelfth.  At  dj  there  are  three  nodes,  ^j,  ^21  ^3>  ^^d 
four  vibrating  sections,  each  vibrating  four  times  as  quickly  as 
the  fundamental  tone,  and  giving  the  second  octave  above  it. 

In  the  same  way  forms  of  vibration  may  occur  with  5,  6,  7, 
&c.,  vibrating  sections,  each  performing  respectively,  5,  6,  7,  &c. 
times  as  many  vibrations  in  a  second  as  the  fundamental  tone, 
and  all  other  vibrational  forms  of  the  string  may  be  conceived  as 
compounded  of  a  sum  of  such  simple  vibrational  forms. 

The  vibrational  forms  with  stationary  points  or  nodes  may  be 
produced,  by  gently  touching  the  string  at  one  of  these  points, 
either  with  the  finger  or  a  rod,  and  rubbing  the  string  with  a 


90 


01^   THE   PHYSIOLOGICAL   CAUSES   OF 


violin  bow,  plucking  it  with  the  finger,  or  striking  it  with  a 
pianoforte  hammer.  The  bell-like  harmonics  or  flageolet-tones 
of  strings,  so  much  used  in  violin  playing,  are  thus  produced. 

No'.v  suppose  that  a  string  has  been  excited,  and  after  its  tone 
has  been  allowed  to  continue  for  a  moment,  it  is  touched  gently 
at  its  middle  point  /3,  Fig.  11  b,  or  ?2>  Fig.  11  d.  The  vibra- 
tional forms  a  and  c,  for  which  this  point  is  in  motion,  will  be 
immediately  checked  and  destroyed ;  but  the  vibrational  forms 
b  and  d,  for  which  this  point  is  at  rest,  will  not  be  disturbed, 
and  the   tones   due  to   them  will    continue   to   be  heard.      In 

Fig.  11. 


this  way  we  can  readily  discover  whether  certain  members  of 
the  series  of  simple  tones  are  contained  in  the  compound  tone  of 
a  string  when  excited  in  any  given  way,  and  the  ear  can  be  ren- 
dered sensible  of  their  existence. 

When  once  these  simple  tones  in  the  sound  of  a  string  have 
been  thus  rendered  audible,  the  ear  will  readily  be  able  to 
observe  them  in  the  untouched  string,  after  a  little  accurate 
attention. 

The  series  of  tones  which  are  thus  made  to  combine  with  a 


HAEMONY   m  MUSIC.  91 

given  fundamental  tone,  is  perfectly  determinate.  They  are  tones 
■which  perform  twice,  thrice,  four  times,  &c.,  as  many  vibrations 
in  a  second  as  the  fundamental  tone.  They  are  called  the  upper 
jmrtialSy  or  harmonic  overtones,  of  the  fundamental  tone.  If 
this  last  be  c,  the  series  may  be  written  as  follows  in  musical 
notation,  [it  being  understood  that,  on  account  of  the  tempera- 
ment of  a  piano,  these  are  not  precisely  the  fundamental  tones  of 
the  corresponding  strings  on  that  instrument,  and  that  in  par- 
ticular the  upper  partial,  h"  b,  is  necessarily  much  flatter  than  the 
fundamental  tone  of  the  corresponding  note  on  the  piano]. 

c        c'  d!       c"       d'      g"      h"\)     c'"     d'"      e'" 

12  3466789         10 

Not  only  strings,  but  almost  all  kinds  of  musical  in- 
struments, produce  waves  of  sound  which  are  more  or  less 
different  from  those  of  simple  tones,  and  are  therefore 
capable  of  being  compounded  out  of  a  greater  or  less 
number  of  simple  waves.  The  ear  analyses  them  all  by 
means  of  Fourier's  theorem  better  than  the  best  mathe- 
matician, and  on  paying  sufficient  attention  can  distin- 
guish the  separate  simple  tones  due  to  the  corresponding 
simple  waves.  This  corresponds  precisely  to  our  theory 
of  the  sympathetic  vibration  of  the  organs  described  by 
Corti.  Experiments  with  the  piano,  as  well  as  the 
mathematical  theory  of  sympathetic  vibrations,  show  that 
any  upper  partials  which  may  be  present  will  also  produce 
sympathetic  vibrations.  It  follows,  therefore,  that  in  the 
cochlea  of  the  ear,  every  external  tone  will  set  in  sympa- 
thetic vibration,  not  merely  the  little  plates  with  their 
accompanying  nerve-fibres,  corresponding  to  its  funda- 
mental tone,  but  also  those  corresponding  to  all  the  upper 
partials,  and  that  consequently  the  latter  must  be  heard 
as  well  as  the  former. 
^  Hence  a  simple  tone  is  one  excited  by  a  succession  of 


92  ON  THE   PHYSIOLOGICAL   CAUSES   OF 

simple  wave-forms.  All  other  wave-forms,  such  as  those 
produced  by  the  greater  number  of  musical  instruments, 
excite  sensations  of  a  variety  of  simple  tones. 

Consequently,  all  the  tones,  of  musical  instruments 
must  in  strict  language,  so  far  as  the  sensation  of  musical 
tone  is  concerned,  be  regarded  as  chords  with  a  pre- 
dominant fundamental  tone. 

The  whole  of  this  theory  of  upper  partials  or  harmonic 
overtones  will  perhaps  seem  new  and  singular.  Probably 
few  or  none  of  those  present,  however  frequently  they 
may  have  heard  or  performed  music,  and  however  fine 
may  be  their  musical  ear,  have  hitherto  perceived  the 
existence  of  any  such  tones,  although,  according  to  my 
representations,  they  must  be  always  and  continuously 
present.  In  fact,  a  peculiar  act  of  attention  is  requisite 
in  order  to  hear  them,  and  unless  we  know  how  to  perform 
this  act,  the  tones  remain  concealed.  As  you  are  aware, 
no  perceptions  obtained  by  the  senses  are  merely  sensa- 
tions impressed  on  our  nervous  systems.  A  peculiar 
intellectual  activity  is  required  to  pass  from  a  nervous 
sensation  to  the  conception  of  an  external  object,  which 
the  sensation  has  aroused.  The  sensations  of  our  nerves 
of  sense  are  mere  symbols  indicating  certain  external 
objects,  and  it  is  usually  only  after  considerable  practice 
that  we  acquire  the  power  of  drawing  correct  conclusions 
from  our  sensations  respecting  the  corresponding  objects. 
Now  it  is  a  universal  law  of  the  perceptions  obtained 
through  the  senses,  that  we  pay  only  so  much  attention  to 
the  sensations  actually  experienced,  as  is  sufficient  for  us 
to  recognise  external  objects.  In  this  respect  we  are  very 
onesided  and  inconsiderate  partisans  of  practical  utility ; 
far  more  so  indeed  than  we  suspect.  All  sensations  which 
have  no  direct  reference  to  external  objects,  we  are  accus- 
tomed, as  a  matter  of  course,  entirely  to  ignore,  and  we 
do  not  become  aware  of  them  till  we  make  a  scientific 


HARMONY   IN   MUSIC.  93 

investigation  of  the  action  of  the  senses,  or  have  our 
attention  directed  by  illness  to  the  phenomena  of  our  own 
bodies.  Thus  we  often  find  patients,  when  suffering  under 
a  slight  inflammation  of  the  eyes,  become  for  the  first 
time  aware  of  those  beads  and  fibres  known  as  mouche^ 
volantes  swimming  about  within  the  vitreous  humour  of 
the  eye,  and  then  they  often  hypochondriacally  imagine 
all  sorts  of  coming  evils,  because  they  fancy  that  these 
appearances  are  new,  whereas  they  have  generally  existed 
all  their  lives. 

Who  can  easily  discover  that  there  is  an  absolutely 
blind  point,  the  so-called  jpunctum  ccecuin,  within  the 
retina  of  every  healthy  eye  ?  How  many  people  know 
that  the  only  objects  they  see  single  are  those  at  which 
they  are  looking,  and  that  all  other  objects,  behind  or 
before  these,  appear  double  ?  I  could  adduce  a  long  list 
of  similar  examples,  which  have  not  been  brought  to 
light  till  the  actions  of  the  senses  were  scientifically  in- 
vestigated, and  which  remain  obstinately  concealed,  till 
attention  has  been  drawn  to  them  by  appropriate  means 
— often  an  extremely  difficult  task  to  accomplish. 

To  this  class  of  phenomena  belong  the  upper  partial 
tones.  It  is  not  enough  for  the  auditory  nerve  to  have  a 
sensation.  The  intellect  must  reflect  upon  it.  Hence 
my  former  distinction  of  a  material  and  a  spiritual  ear. 

We  always  hear  the  tone  of  a  string  accompanied  by  a 
certain  combination  of  upper  partial  tones.  A  diff*erent 
combination  of  such  tones  belongs  to  the  tone  of  a  flute, 
or  of  the  human  voice,  or  of  a  dog's  howl.  Whether  a 
violin  or  a  flute,  a  man  or  a  dog  is  close  by  us  is  a  matter 
of  interest  for  us  to  know,  and  our  ear  takes  care  to  dis- 
tinguish the  peculiarities  of  their  tones  with  accuracy. 
The  means  by  which  we  can  distinguish  them,  however, 
is  a  matter  of  perfect  indifference. 

Whether  the  cry  of  the  dog  contains  the  higher  octave 


94  ox  THE   PHYSIOLOGICAL   CAUSES   OF 

or  the  twelfth  of  the  fundamental  tone,  has  no  practical 
interest  for  us,  and  never  occupies  our  attention.  The 
upper  partials  are  consequently  thrown  into  that  un- 
analysed  mass  of  peculiarities  of  a  tone  which  we  call  its 
quality.  Now  as  the  existence  of  upper  partial  tones 
depends  on  the  wave  form,  we  see,  as  I  was  able  to 
state  previously  (p.  74),  that  the  quality  of  tone  corre- 
sponds to  the  foTTn  of  wave. 

The  upper  partial  tones  are  most  easily  heard  when 
they  are  not  in  harmony  with  the  fundamental  tone,  as 
in  the  case  of  bells.  The  art  of  the  bell-founder  consists 
precisely  in  giving  bells  such  a  form  that  the  deeper  and 
stronger  partial  tones  shall  be  in  harmony  with  the 
fundamental  tone,  as  otherwise  the  bell  would  be  un- 
musical, tinkling  like  a  kettle.  But  the  higher  partials 
are  always  out  of  harmony,  and  hence  bells  are  unfitted 
for  artistic  music. 

On  the  other  hand,  it  follows,  from  what  has  been  said, 
that  the  upper  partial  tones  are  all  the  more  difficult  to 
hear,  the  more  accustomed  we  are  to  the  compound  tones 
of  which  they  form  a  part.  This  is  especially  the  case 
with  the  human  voice,  and  many  skilful  observers  have 
consequently  failed  to  discover  them  there. 

The  preceding  theory  was  wonderfully  corroborated  by 
leading  to  a  method  by  which  not  only  I  myself,  but 
other  persons,  were  enabled  to  hear  the  upper  partial 
tones  of  the  human  voice. 

No  particularly  fine  musical  ear  is  required  for  this 
purpose,  as  was  formerly  supposed,  but  only  proper  means 
for  directing  the  attention  of  the  observer. 

Let  a  powerful  male  voice  sing  the  note  e  b  ^:-t?y-  to 

the  vowel  o  in  ore,  close  to  a  good  piano.     Then  lightly 

touch  on  the  piano  the  note  V  b  'W^^  in  the  next  octave 


HAKMONY  m  MUSIC.  95 

above,  and  listen  attentively  to  the  sound  of  the  piano  as 
it  dies  away.  If  this  6'  (7  is  a  real  upper  partial  in  the 
compound  tone  uttered  by  the  singer,  the  sound  of  the 
piano  will  apparently  not  die  away  at  all,  but  the  corre- 
sponding upper  partial  of  the  voice  will  be  heard  as  if 
the  note  of  the  piano  continued.*  By  properly  varying 
the  experiment,  it  will  be  found  possible  to  distinguish 
the  vowels  from  one  another  by  their  upper  partial  tones. 
The  investigation  is  rendered  much  easier  by  arming 
the  ear  with  small  globes  of  glass  or  metal,  as  in  Fig.  12. 

Fig.  12. 


.n;\ 


The  larger  opening  a  is  directed  to  the  source  of  sound, 
and  the  smaller  funnel-shaped  end  is  applied  to  the  drum 
of  the  ear.  The  enclosed  mass  of  air,  which  is  almost 
entirely  separated  from  that  without,  has  its  own  proper 
tone  or  key-note,  which  w411  be  heard,  for  example,  on 
blowing  across  the  edge  of  the  opening  a.  If  then  this 
proper  tone  of  the  globe  is  excited  in  the  external  air, 
either  as  a  fundamental  or  upper  partial  tone,  the  in- 

'  In  repeating  this  experiment  the  observer  must  rememher  that  the  e  & 
of  the  piano  is  not  a  true  twelfth  below  the  //fe.  Hence  the  singer  should 
first  be  given  6' fe  from  the  piano,  which  he  will  naturally  sing  as  ia,  an 
octave  lower,  and  then  take  a  true  fifth  below  it.  A  skilful  singer  will 
thus  hit  the  true  twelfth  and  produce  the  required  upper  partial  b'k.  On 
the  other  hand,  if  he  sings  e  h.  from  the  piano,  his  upper  partial  b'  b  -will 
probably  beat  with  that  of  the  piano. — Tb. 


96  ox  THE   PHYSIOLOGICAL  CAUSES   OF 

eluded  mass  of  air  is  brought  into  violent  sympathetic 
vibration,  and  the  ear  thus  connected  with  it  hears  the 
corresponding  tone  with  much  increased  intensity.  By 
this  means  it  is  extremely  easy  to  determine  whether  the 
proper  tone  of  the  globe  is  or  is  not  contained  in  a 
compound  tone  or  mass  of  tones. 

On  examining  the  vowels  of  the  human  voice,  it  is  easy 
to  recognise,  with  the  help  of  such  resonators  as  have  just 
been  described,  that  the  upper  partial  tones  of  each  vowel 
are  peculiarly  strong  in  certain  parts  of  the  scale :  thus 
0  in  ore  has  its  upper  partials  in  the  neighbourhood  of 
h'  [2,  A  in  father  in  the  neighbourhood  of  h"  b  (an  octave 
higher).  The  following  gives  a  general  view  of  those 
portions  of  the  scale  where  the  upper  partials  of  the 
vowels,  as  pronounced  in  the  north  of  Germany,  are  par- 
ticularly strong. 


Names  of  Notes. 
/             6'l2 

^b"h 

:(?-6"  h   ; 

^d"^ 

^d"t 

r 

tIS — — 



— 1 

— tr— 

1 

1                  1 

^' — 1— 

f- 

— i 

la 

t— 

f" 

— 1 — 

u 

'   00 

in 
cool 

Dondere  /' 

0 

0 

in 

ore 

nearly 

d 

A 
a 

in 

Scotch 
nearly 

b'h 

A 
a 
in 
fat 
nearly 

E 
a 

in              ] 
fflte           f 
nearly 
C'Jf 

ee 
n 

sel 

fin 

t/' 

6 

eu 

in 
French 
nearly 

1- 

u 

in 
French 
nearly 

a" 

*  The  corresponding  English  vowel  sounds  are  probably  none  of  them 
precisely  the  same  as  those  pronounced  by  the  author.  It  is  necessary  to 
note  this,  for  a  very  slight  variation  in  pronunciation  would  produce  a 
change  in  the  fundamental  tone,  and  consequently  a  more  considerable 
change  in  the  position  of  the  upper  partials.  The  tones  given  by  Dunders, 
which  are  written  below  the  English  equivalents,  are  cited  on  the  authority 
of  Helmholtz's  Tonempjindungen,  3rd  edition,  1870,  p.  171,  where  Helm- 
holtz  says :  '  Donders's  results  differ  somewhat  from  mine,  partly  because 
his  refer  to  a  Dutch,  and  mine  to  a  North  German  pronunciation,  and  partly 
because  Donders,  not  having  had  the  assistance  of  tuning  forks,  could  net 
always  correctly  determine  the  octave  to  which  the  sounds  belong,'  Also 
{ih.  p.  167)  the  author  remarks  that  h"  fe  answers  only  to  the  deep  German 
a  (which  is  the  broad  Scotch  a\  or  aw  without  labialisation),  and  that  if  the 
brighter  Italian  a  (English  a  in  father)  be  used,  the  resonance  rises  a  third, 
to  d'".     Dr.  C.  L.  Merkel,  of  Leipzig,  in  his  Physiologic  der  menschlichtn 


HAEMONY   IN  MUSIC.  97 

The  following  easy  experiment  clearly  shows  that  it  is 
indifferent  whether  the  several  simple  tones  contained  in 
a  compound  tone  like  a  vowel  uttered  by  the  human  voice 
come  from  one  source  or  several.  If  the  dampers  of  a 
pianoforte  are  raised,  not  only  do  the  sympathetic  vibra- 
tions of  the  strings  furnish  tones  bf  the  same  jpitch  as 
those  uttered  beside  it ;  but  if  we  sing  A  («  in  father)  to 
any  note  of  the  piano,  we  hear  an  A  quite  clearly  re- 
turned from  the  strings ;  and  if  E  (a  in  fare  or  fate),  0 
(o  in  hole  or  ore),  and  U  {oo  in  cool\  be  similarly  sung  to 
the  note,  E,  0,  and  U  will  also  be  echoed  back.  It  is 
only  necessary  to  hit  the  note  of  the  piano  with  great 
exactness.^     Now  the   sound  of  the  vowel   is   produced 

Sprache,  1866,  p.  109,  after  citing  Helmholtz's  experiments  as  detailed  in 
his  Tonempfinduvgen,  gives  the  following  as  *  the  pitches  of  the  vowels 
according  to  his  most  recent  examination  of  his  own  habits  of  speech,  as 
accurately  as  he  is  able  to  note  them.' 


v^.g          I— 

— -^=^*-  - 

A« 

1 

=-p f- 

^•:Sjri= 

-A 

1 — 

Z-&— ^^ 

B=-^= 

— ^ 

=S^ 

— 1 

1 

U 

0 

0^ 

t 
A          A 

0 

a 

1 

A 

E 

E          I 

00 

0 

0 

a           a 

eu 

u 

a 

a 

a         ee 

jn 

in 

in 

in          in 

in 

in 

in 

in 

in        in 

cool 

hole 

ore 

Scotch  father 
man 

French 

French 

fat 
V 

fare 

fate       feel 

nearly 

'  Here  the  note  a  applies  to  the  timbre  ohscur  of  A  with  low  larynx,  and 
h  to  the  timbre  clair  of  A  with  high  larynx,  and  similarly  the  vowel  E  may 
pass  from  d"  to  e"  by  narrowing  the  channel  in  the  muulh.  The  interme- 
diate vowels  O,  A,  have  also  two  different  timbres  and  hence  their  pitch  is 
not  fixed  ;  the  most  frequent  are  consequently  written  over  one  another ; 
the  lower  note  is  for  the  obscure,  and  the  higher  for  the  bright  timbre. 
But  the  vowel  tj  seems  to  be  tolerably  fixed  as  a',  just  as  its  parents  U  and 
I  are  upon  d  and  a",  and  it  has  consequently  the  pitch  of  the  ordinary  a' 
tuning  fork.' — Tb. 

'  My  own  experience  shows  that  if  any  vowel  at  any  pitch  be  loudly  and 
sharply  sung,  or  called  out,  beside  a  piano,  of  which  the  dampers  have  been 
raised,  that  vowel  will  be  echoed  back.  There  is  generally  a  sensible  pause 
before  the  echo  is  heard.  Before  repeating  the  experiment  with  a  new 
vowel,  whether  at  the  same  or  a  different  pitch,  damp  all  the  strings  and 
then  again  raise  the  dampers.  The  result  can  easily  be  made  audible  to  a 
hundred  persons  at  once,  and  it  is  extremely  interesting  and  instructive.  It 
is  peculiarly  so,  if  different  vowels  be  sung  to  the  same  pitch,  so  that  they 


98  OJf   THE   PHYSIOLOGICAL   CAUSES   OF 

solely  by  the  sympathetic  vibration  of  the  higher  strings, 
which  correspond  with  the  upper  partial  tones  of  the  tone 
sung. 

In  this  experiment  the  tones  of  numerous  strings  are 
excited  by  a  tone  proceeding  from  a  single  source,  the 
human  voice,  which  produces  a  motion  of  the  air,  equi- 
valent in  form,  and  therefore  in  quality,  to  that  of  this 
single  tone  itself. 

We  have  hitherto  spoken  only  of  compositions  of  waves 
of  different  lengths.  We  will  now  compound  waves  of 
the  same  length  which  are  moving  in  the  same  direction. 
The  result  will  be  entirely  different,  according  as  the 
elevations  of  one  coincide  with  those  of  the  other  (in 
which  case  elevations  of  double  the  height  and  depres- 
sions of  double  the  depth  are  produced),  or  the  elevations 
of  one  fall  on  the  depressions  of  the  other.  If  both 
waves  have  the  same  height,  so  that  the  elevations  of  one 
exactly  fit  into  the  depressions  of  the  other,  both  eleva- 
tions and  depressions  will  vanish  in  the  second  case,  and 
the  two  waves  will  mutually  destroy  each  other.  Simi- 
larly two  waves  of  sound,  as  well  as  two  waves  of  water, 
may  mutually  destroy  each  other,  when  the  condensations 
of  one  coincide  with  the  rarefactions  of  the  other.  This 
remarkable  phenomenon  wherein  sound  is  silenced  by  a 
precisely  similar  sound,  is  called  the  interference  of 
sounds. 

This  is  easily  proved  by  means  of  the  siren  already 
described.  On  placing  the  upper  box  so  that  the  puffs  of 
air  may  proceed  simultaneously  from  the  rows  of  twelve 
holes  in  each  wind  chest,  their  effect  is  reinforced,  and 

have  all  the  same  fundamental  tone,  and  the  upper  partials  only  differ  in 

intensity.     For  female  voices  the  pitches  T^-r^—^  a'  to  c"  are  favourable 

for  all  vowels.  This  is  a  fundamental  experiment  for  the  theory  of  vowel 
sounds,  and  should  be  repeated  by  all  who  are  interested  in  speech. — Tb. 


HAEMOFT  m  MUSIC.  99 

we  obtain  the  fundamental  tone  of  the  corresponding 
tone  of  the  siren  very  full  and  strong.  But  on  arranging 
the  boxes  so  that  the  upper  puffs  escape  when  the  lower 
series  of  holes  is  covered,  and  conversely,  the  fundamental 
tone  vanishes,  and  we  only  hear  a  faint  sound  of  the  first 
upper  partial,  which  is  an  octave  higher,  and  which  is  not 
destroyed  by  interference  under  these  circumstances. 

Interference  leads  us  to  the  so-called  musical  beats. 
If  two  tones  of  exactly  the  same  pitch  are  produced 
simultaneously,  and  their  elevations  coincide  at  first,  they 
will  never  cease  to  coincide,  and  if  they  did  not  coincide 
at  first  they  never  will  coincide. 

The  two  tones  will  either  perpetually  reinforce,  or  per- 
petually destroy  each  other.  But  if  the  two  tones  have  only 
approximatively  equal  pitches,  and  their  elevations  at 
first  coincide,  so  that  they  mutually  reinforce  each  other, 
the  elevations  of  one  will  gradually  outstrip  the  elevations 
of  the  other.  Times  will  come  when  the  elevations  of  the 
one  fall  upon  the  depressions  of  the  other,  and  then  other 
times  when  the  more  rapidly  advancing  elevations  of  the 
one  will  have  again  reached  the  elevations  of  the  other. 
These  alternations  become  sensible  by  that  alternate 
increase  and  decrease  of  loudness,  which  we  call  a  beat. 
These  beats  may  often  be  heard  when  two  instruments 
which  are  not  exactly  in  unison  play  a  note  of  the  same 
name.  When  the  two  or  three  strings  which  are  struck 
by  the  same  hammer  on  a  piano  are  out  of  tune,  the  beats 
may  be  distinctly  heard.  Very  slow  and  regular  beats 
often  produce  a  fine  eflfect  in  sostenuto  passages,  as  in 
sacred  part-songs,  by  pealing  through  the  lofty  aisles  like 
majestic  waves,  or  by  a  gentle  tremour  giving  the  tone  a 
character  of  enthusiasm  and  emotion.  The  greater  the 
diflference  of  the  pitches,  the  quicker  the  beats.  As  long 
as  no  more  than  four  to  six  beats  occur  in  a  second, 
the  ear  readily  distinguishes  the  alternate  reinforcements 


100  ON   THE   PHYSIOLOGICAL   CAUSES   OF 

of  the  tone.  If  the  beats  are  more  rapid  the  tone  grates 
on  the  ear,  or,  if  it  is  high,  becomes  cutting.  A  grating 
tone  is  one  interrupted  by  rapid  breaks,  like  that  of  the 
letter  K,  which  is  produced  by  interrupting  the  tone  of 
the  voice  by  a  tremour  of  the  tongue  or  uvula.^ 

When  the  beats  become  more  rapid,  the  ear  finds  a 
continually-increasing  difficulty  when  attempting  to  hear 
them  separately,  even  though  there  is  a  sensible  rough- 
ness of  the  tone.  At  last  they  become  entirely  undis- 
tinguishable,  and,  like  the  separate  puffs  which  compose 
a  tone,  dissolve  as  it  were  into  a  continuous  sensation 
of  tone.'^ 

Hence,  while  every  separate  musical  tone  excites  in 
the  auditory  nerve  a  uniform  sustained  sensation,  two 
tones  of  different  pitches  mutually  disturb  one  another, 
and  split  up  into  separable  beats,  which  excite  a  feeling 
of  discontinuity  as  disagreeable  to  the  ear  as  similar 
intermittent  but  rapidly  repeated  sources  of  excitement 
are  unpleasant  to  the  other  organs  of  sense  ;  for  example, 
flickering  and  glittering  light  to  the  eye,  scratching  with 
a  brush  to  the  skin.  This  roughness  of  tone  is  the  es- 
sential character  of  dissonance.  It  is  most  unpleasant  to 
the  ear  when  the  two  tones  differ  by  about  a  semitone,  in 
which  case,  in  the  middle  portions  of  the  scale,  from  twenty 
to  forty  beats  ensue  in  a  second.  When  the  difference  is 
a  whole  tone,  the  roughness  is  less  ;  and  when  it  reaches 
a  third  it  usually  disappears,  at  least  in  the  higher  parts 
of  the  scale.     The  (minor  or  major)  third  may  in  conse- 

'  The  trill  of  the  uvula  is  called  the  Northumbrian  burr,  and  is  not 
known  out  of  Northumberland,  in  England.  In  France  it  is  called  the 
r  grass^nje,  or  j>rQve7i^al,  and  is  the  commonest  Parisian  sound  of  r.  The 
uvula  trill  is  also  very  common  in  Germany,  but  it  is  quite  unknown  in 
Italy.— Tb. 

'^  The  transition  of  beats  into  a  harsh  dissonance  was  displayed  by  means 
of  two  organ  pipes,  of  which  one  was  gradually  put  more  and  more  out  of 
tune  with  the  other. 


HAEMONY   m  MUSIC.  101 

quence  pass  as  a  consonance.  Even  when  the  fund  imental 
tones  have  such  widely-different  pitches  that  they  cannot 
produce  audible  beats,  the  upper  partial  tones  may  beat 
and  make  the  tone  rough.  Thus,  if  two  tones  form  a 
fifth  (that  is,  one  makes  two  vibrations  in  the  same  time 
as  the  other  makes  three),  there  is  one  upper  partial  in 
both  tones  which  makes  six  vibrations  in  the  same  time. 
Now,  if  the  ratio  of  the  pitches  of  the  fundamental  tones 
is  exactly  as  2  to  3,  the  two  upper  partial  tones  of  six 
vibrations  are  precisely  alike,  and  do  not  destroy  the 
harmony  of  the  fundamental  tones.  But  if  this  ratio  is 
only  approximatively  as  2  to  3,  then  these  two  upper 
partials  are  not  exactly  alike,  and  hence  will  beat  and 
roughen  the  tone. 

It  is  very  easy  to  hear  the  beats  of  such  imperfect 
fifths,  because,  as  our  pianos  and  organs  are  now  tuned, 
all  the  fifths  are  impure,  although  the  beats  are  very 
slow.  By  properly  directed  attention,  or  still  better 
with  the  help  of  a  properly  tuned  resonator,  it  is  easy  to 
hear  that  it  is  the  particular  upper  partials  here  spoken 
of,  that  are  beating  together.  The  beats  are  necessarily 
weaker  than  those  of  the  fundamental  tones,  because  the 
beating  upper  partials  are  themselves  weaker.  Although 
we  are  not  usually  clearly  conscious  of  these  beating 
upper  partials,  the  ear  feels  their  effect  as  a  want  of 
uniformity  or  a  roughness  in  the  mass  of  tone,  whereas 
a  perfectly  pure  fifth,  the  pitches  being  precisely  in  the 
ratio  of  2  to  3,  continues  to  sound  with  perfect  smooth- 
ness, without  any  alterations,  reinforcements,  diminutions, 
or  roughnesses  of  tone.  As  has  already  been  mentioned, 
the  siren  proves  in  the  simplest  manner  that  the  most 
perfect  consonance  of  the  fifth  precisely  corresponds  to 
this  ratio  between  the  pitches.  We  have  now  learned 
the  reason  of  the  roughness  experienced  when  any  devia- 
tion from  that  ratio  has  been  produced. 


102  ON  THE   PHYSIOLOGICAL   CAUSES   OF 

Tn  the  same  way  two  tones,  which  have  their  pitches 
exactly  in  the  ratios  of  3  to  4,  or  4  to  5,  and  consequently 
form  a  perfect  fourth  or  a  perfect  major  third,  sound 
much  better  when  sounded  together,  than  two  others  of 
which  the  pitches  slightly  deviate  from  this  exact  ratio. 
In  this  manner,  then,  any  given  tone  being  assumed  as 
fundamental,  there  is  a  precisely  determinate  number  of 
other  degrees  of  tone  which  can  be  sounded  at  the  same 
time  with  it,  without  producing  any  want  of  uniformity 
or  any  roughness  of  tone,  or  which  will  at  least  produce 
less  roughness  than  any  slightly  greater  or  smaller  inter- 
vals of  tone  under  the  same  circumstances. 

This  is  the  reason  why  modem  music,  which  is  essen- 
tially based  on  the  harmonious  consonance  of  tones,  has 
been  compelled  to  limit  its  scale  to  certain  determinate 
degrees.  But  even  in  ancient  music,  which  allowed  only 
one  part  to  be  sung  at  a  time,  and  hence  had  no  harmony 
in  the  modern  sense  of  the  word,  it  can  be  shown  that 
the  upper  partial  tones  contained  in  all  musical  tones 
sufficed  to  determine  a  preference  in  favour  of  pro- 
gressions through  certain  determinate  intervals.  When 
an  upper  partial  tone  is  common  to  two  successive  tones 
in  a  melody,  the  ear  recognises  a  certain  relationship 
between  them,  serving  as  an  artistic  bond  of  union. 
Time  is,  however,  too  short  for  me  to  enlarge  on  this 
topic,  as  we  should  be  obliged  to  go  far  back  into  the 
history  of  music. 

I  will  but  mention  that  there  exists  another  kind  of 
secondary  tones,  which  are  only  heard  when  two  or  more 
loudish  tones  of  different  pitch  are  sounded  together,  and 
are  hence  termed  combinational.^     These  secondary  tones 

•  These  are  of  two  kinds,  differential  and  summaiional,  according  as  their 
pitch  is  the  difference  or  sum  of  the  pitches  of  the  two  generating  tones. 
The  former  are  the  only  combinational  tones  here  spoken  of.  The  dis- 
covery of  the  latter  was  entirely  due  to  the  theoretical  investigations  of  the 
author. — Tn. 


HAEMOFT  IN  MUSIC.  103 

are  likewise  capable  of  beating,  and  hence   producing 
roughness  in  the  chords.     Suppose  a  perfectly  just  major 

third  c'  e'  S=^  (ratio  of  pitches,  4  to  5)  is  sounded  on 
the  siren,  or  with  properly-tuned  organ  pipes,  or  on  a 

violin;^  then  a  faint  C   ^^^^^  two  octaves  deeper  than 
the  c'  will  be  heard  as  a  combinational  tone.     The  same 


C  is  also  heard   when  the   tones   e'  g'  m=^  (ratio   of 
pitches  5  to  6)  are  sounded  together.^ 

If  the  three  tones  c\  e\  g\  having  their  pitches  precisely 
in  the  ratios  4,  5,  and  6,  are  struck  together,  the  com- 
binational tone  C  is  produced  twice  ^  in  perfect  unison, 
and  without  beats.  But  if  the  three  notes  are  not 
.  exactly  thus  tuned,'*  the  two  C  combinational  tones  will 
have  different  pitches,  and  produce  faint  beats. 

The  combinational  tones  are  usually  much  weaker  than 
the  upper  partial  tones,  and  hence  their  beats  are  much 
less  rough  and  sensible  than  those  of  the  latter.  They 
are  consequently  but  little  observable,  except  in  tones 
which  have  scarcely  any  upper  partials,  as  those  produced 
by  flutes  or  the  closed  pipes  of  organs.  But  it  is  indisput- 
able that  on  such  instruments  part-music  scarcely  presents 
any  line  of  demarcation  between  harmony  and  dyshar- 
mony,  and  is  consequently  deficient  both  in  strength  and 
character.  On  the  contrary,  all  good  musical  qualities  of 
tone  are  comparatively  rich  in  upper  partials,  possessing 

*  In  the  ordinary  tuning  of  the  English  concertina  this  major  third  is 
just,  and  generally  this  instrument  shows  the  differential  tones  very  \yell. 
The  major  third  is  very  false  on  the  harmonium  and  piano. — Tr. 

2  This  minor  third  is  very  false  on  the  English  concertina,  harmonium,  or 
piano,  and  the  combinational  tone  heard  is  consequently  very  different 
from  the  true  C— Ta, 

3  The  combinational  tone  c,  an  octave  higher,  is  also  produced  once 
from  the  fifth  d  ^'.— Tr. 

*  As  on  the  English  concertina  or  harmonium,  on  both  of  which  the  con- 
sequent effect  may  be  well  heard. — Tb. 


104  ox   THE   PHYSIOLOGICAL   CAUSES   OF 

the  five  first,  which  form  the  octaves,  fifths,  and  major 
thirds  of  the  fundamental  tone.  Hence,  in  the  mixture 
stops  of  the  organ,  additional  pipes  are  used,  giving  the 
series  of  upper  partial  tones  corresponding  to  the  pipe 
producing  the  fundamental  tone,  in  order  to  generate  a 
penetrating,  powerful  quality  of  tone  to  accompany  con- 
gregational singing.  The  important  part  played  by  the 
upper  partial  tones  in  all  artistic  musical  effects  is  here 
also  indisputable. 

We  have  now  reached  the  heart  of  the  theory  of  har- 
mony. Harmony  and  dysharmony  are  distinguished  by 
the  undisturbed  current  of  the  tones  in  the  former, 
which  are  as  flowing  as  when  produced  separately,  and 
by  the  disturbances  created  in  the  latter,  in  which  the 
tones  split  up  into  separate  beats.  All  that  we  have 
considered,  tends  to  this  end.  In  the  first  place  the 
phenomenon  of  beats  depends  on  the  interference  of 
waves.  Hence  they  could  only  occur,  if  sound  were  due 
to  undulations.  Next,  the  determination  of  consonant 
intervals  necessitated  a  capability  in  the  ear  of  feeling 
the  upper  partial  tones,  and  analysing  the  compound 
systems  of  waves  into  simple  undulations,  according  to 
Fourier's  theorem.  It  is  entirely  due  to  this  theorem 
that  the  pitches  of  the  upper  partial  tones  of  all  service- 
able musical  tones  must  stand  to  the  pitch  of  their  fun- 
damental tones  in  the  ratios  of  the  whole  numbers  to  1, 
and  that  consequently  the  ratios  of  the  pitches  of  con- 
cordant intervals  must  correspond  with  the  smallest 
possible  whole  numbers.  How  essential  is  the  physio- 
logical constitution  of  the  ear  which  we  have  just 
considered,  becomes  clear  by  comparing  it  with  that  of 
the  eye.  Light  is  also  an  undulation  of  a  peculiar 
medium,  the  luminous  ether,  diffused  through  the  uni- 
verse, and  light,  as  well  as  sound,  exhibits  phenomena  of 
interference.     Light,  too,  has  waves  of  various  periodic 


HARMOifr  IN  MUSIC.  105 

times  of  vibration,  which  produce  in  the  eye  the  sensation 
of  colour,  red  having  the  greatest  periodic  time,  then 
orange,  yellow,  green,  blue,  violet ;  the  periodic  time  of 
violet  being  about  half  that  of  the  outermost  red.  But 
the  eye  is  unable  to  decompose  compound  systems  of 
luminous  waves,  that  is,  to  distinguish  compound  colours 
from  one  another.  It  experiences  from  them  a  single, 
unanalysable,  simple  sensation,  that  of  a  mixed  colour. 
It  is  indifferent  to  the  eye  whether  this  mixed  colour 
results  from  a  union  of  fundamental  colours  with  simple, 
or  with  non-simple  ratios  of  periodic  times.  The  eye  has 
no  sense  of  harmony  in  the  same  meaning  as  the  ear. 
There  is  no  music  to  the  eye. 

Esthetics  endeavour  to  find  the  principle  of  artistic 
beauty  in  its  unconscious  conformity  to  law.  To-day  I 
have  endeavoured  to  lay  bare  the  hidden  law,  on  which  de- 
pends the  agreeableness  of  consonant  combinations.  It  is 
in  the  truest  sense  of  the  word  unconsciously  obeyed,  so 
far  as  it  depends  on  the  upper  partial  tones,  which, 
though  felt  by  the  nerves,  are  not  usually  consciously 
present  to  the  mind.  Their  compatibility  or  incom- 
patibility however  is  felt,  without  the  hearer  knowing 
the  cause  of  the  feeling  he  experiences. 

These  phenomena  of  agreeableness  of  tone,  as  deter- 
mined solely  by  the  senses,  are  of  course  merely  the  first 
step  towards  the  beautiful  in  music.  For  the  attainment 
of  that  higher  beauty  which  a^opeals  to  the  intellect, 
harmony  and  dysharmony  are  only  means,  although  essen- 
tial and  powerful  means.  In  dysharmony  the  auditory 
nerve  feels  hurt  by  the  beats  of  incompatible  tones.  It 
longs  for  the  pure  efflux  of  the  tones  into  harmony.  It 
hastens  towards  that  harmony  for  satisfaction  and  rest. 
Thus  both  harmony  and  dysharmony  alternately  urge  and 
moderate  the  flow  of  tones,  while  the  mind  sees  in  their 
immaterial   motion   an    image   of    its   own   perpetually 


106     THE   PHYSIOLOGICAL   CAUSES    OF   HAEMONT. 

streaming  thoughts  and  moods.  Just  as  in  the  rolling 
ocean,  this  movement,  rhythmically  repeated,  and  yet 
ever  varying,  rivets  our  attention  and  hurries  us  along. 
But  whereas  in  the  sea,  blind  physical  forces  alone  are  at 
"work,  and  hence  the  final  impression  on  the  spectator's 
mind  is  nothing  but  solitude — in  a  musical  work  of  art 
the  movement  follows  the  outflow  of  the  artist's  own 
emotions.  Now  gently  gliding,  now  gracefully  leaping, 
now  violently  stirred,  penetrated  or  laboriously  contend- 
ing with  the  natural  expression  of  passion,  the  stream  of 
sound,  in  primitive  vivacity,  bears  over  into  the  hearer's 
soul  unimagined  moods  which  the  artist  has  overheard 
from  his  own,  and  finally  raises  him  up  to  that  repose  of 
everlasting  beauty,  of  which  Grod  has  allowed  but  few  of 
his  elect  favourites  to  be  the  heralds. 

But  I  have  reached  the  confines  of  physical  science, 
and  must  close. 


ICE  AND   GLACIERS. 

A   LECTURE   DELIVERED   AT  FRANKFORT-ON-THE-MAIN,   AND   AT 
HEIDELBERG,  IN   FEBRUARY   1865. 


The  world  of  ice  and  of  eternal  snow,  as  unfolded  to  us 
on  the  summits  of  the  neighbouring  Alpine  chain,  so 
stern,  so  solitary,  so  dangerous,  it  may  be,  has  yet  its  own 
peculiar  charm.  Not  only  does  it  enchain  the  attention  of 
the  natural  philosopher,  who  finds  in  it  the  most  wonderful 
disclosures  as  to  the  present  and  past  history  of  the  globe, 
but  every  summer  it  entices  thousands  of  travellers  of  all 
conditions,  who  find  there  mental  and  bodily  recreation. 
While  some  content  themselves  with  admiring  from  afar 
the  dazzling  adornment  which  the  pure,  luminous  masses 
of  snowy  peaks,  interposed  between  the  deeper  blue  of 
the  sky  and  the  succulent  green  of  the  meadows,  lend  to 
the  landscape,  others  more  boldly  penetrate  into  the 
strange  world,  willingly  subjecting  themselves  to  the 
most  extreme  degrees  of  exertion  and  danger,  if  only 
they  may  fill  themselves  with  the  aspect  of  its  sublimity. 

I  will  not  attempt  what  has  so  often  been  attempted  in 
vain — to  depict  in  words  the  beauty  and  magnificence  of 
nature,  whose  aspect  delights  the  Alpine  traveller.  I 
may  well  presume  that  it  is  known  to  most  of  you  from 
your  own  observation ;  or,  it  is  to  be  hoped,  will  be 
so.  But  I  imagine  that  the  delight  and  interest  in  the 
6 


108  ICE   AXD   GLACIERS. 

mag-nificence  of  tliose  scenes  will  make  you  the  more 
inclined  to  lend  a  willing  ear  to  the  remarkable  results  of 
modern  investigations  on  the  more  prominent  phenomena 
of  the  glacial  world.  There  we  see  that  minute  pecu- 
liarities of  ice,  the  mere  mention  of  which  might  at  other 
times  be  regarded  as  a  scientific  subtlety,  are  the  causes  of 
the  most  important  changes  in  glaciers  ;  shapeless  masses 
of  rock  begin  to  relate  their  histories  to  the  attentive  ob- 
server, histories  which  often  stretch  far  beyond  the  past  of 
the  human  race  into  the  obscurity  of  the  primeval  world ; 
a  peaceful,  uniform,  and  beneficent  sway  of  enormous 
natural  forces,  where  at  first  sight  only  desert  wastes  are 
seen,  either  extended  indefinitely  in  cheerless,  desolate 
solitudes,  or  full  of  wild,  threatening  confusion — an  arena 
of  destructive  forces.  And  thus  I  think  I  may  promise 
that  the  study  of  the  connection  of  those  phenomena  of 
which  I  can  now  only  give  you  a  very  short  outline  will 
not  only  afford  you  some  prosaic  instruction,  but  will 
make  your  pleasure  in  the  magnificent  scenes  of  the  high 
mountains  more  vivid,  your  interest  deeper,  and  your 
admiration  more  exalted. 

Let  me  first  of  all  recall  to  your  remembrance  the  chief 
features  of  the  external  appearance  of  the  snow-fields  and 
of  the  glaciers ;  and  let  me  mention  the  accurate 
measurements  which  have  contributed  to  supplement  ob- 
servation, before  I  pass  to  discuss  the  causal  connection  of 
those  processes. 

The  higher  we  ascend  the  mountains  the  colder  it  becomes. 
Our  atmosphere  is  like  a  warm  covering  spread  over  the 
earth  ;  it  is  well-nigh  entirely  transparent  for  the  lumi- 
nous darting  rays  of  the  sun,  and  allows  them  to  pass  almost 
without  appreciable  change.  But  it  is  not  equally  pene- 
trable by  obscure  heat-rays,  which,  proceeding  from  heated 
terrestrial  bodies,  struggle  to  diffuse  themselves  into  space. 
These  are  absorbed  by  atmospheric  air,  especially  when  it 


ICE  AND   GLACIERS.  .  109 

is  moist ;  the  mass  of  air  is  itself  heated  thereby,  and 
only  radiates  slowly  into  space  the  heat  which  has  been 
gained.  The  expenditure  of  heat  is  thus  retarded  as  com- 
pared with  the  supply,  and  a  certain  store  of  heat  is 
retained  along  the  whole  surface  of  the  earth.  But  on 
high  mountains  the  protective  coating  of  the  atmosphere 
is  far  thinner — the  radiated  heat  of  the  ground  can  escape 
thence  more  freely  into  space ;  there,  accordingly,  the 
accumulated  store  of  heat  and  the  temperatm'e  are  far 
smaller  than  at  lower  levels. 

To  this  must  be  added  another  property  of  air  which 
acts  in  the  same  direction.  In  a  mass  of  air  which  ex- 
pands, part  of  its  store  of  heat  disappears ;  it  becomes 
cooler,  if  it  cannot  acquire  fresh  heat  from  without. 
Conversely,  by  renewed  compression  of  the  air,  the  same 
quantity  of  heat  is  reproduced  which  had  disappeared  du- 
ring expansion.  Thus  if,  for  instance,  south  winds  drive 
the  warm  air  of  the  Mediterranean  towards  the  north,  and 
compel  it  to  ascend  along  the  great  mountain-wall  of  the 
Alps,  where  the  air,  in  consequence  of  the  diminished 
pressure,  expands  by  about  half  its  volume,  it  thereby 
becomes  very  greatly  cooled — for  a  mean  height  of  11,000 
feet,  by  from  18°  to  30°  C,  according  as  it  is  moist  or  dry — • 
and  it  thereby  deposits  the  greater  part  of  its  moisture  as 
rain  or  snow.  If  the  same  wind,  passing  over  to  the  north 
side  of  the  mountains  as  Fohn-wind,  reaches  the  valleys 
and  plains,  it  again  becomes  condensed,  and  is  again 
heated.  Thus  the  same  current  of  air  which  is  warm  in 
the  plains,  both  on  this  side  of  the  chain  and  on  the  other, 
is  bitterly  cold  on  the  heights,  and  can  there  deposit  snow, 
while  in  the  plain  we  find  it  insupportably  hot. 

The  lower  temperature  at  greater  heights,  which  is  due 
to  both  these  causes,  is,  as  we  know,  very  marked  on  the 
lower  mountain  chains  of  our  neighbourhood.  In  central 
Europe  it  amounts  to  about  1°  C.  for  an  ascent  of  480  feet; 


110  ICE   AXD    GLACIERS. 

in  winter  it  is  less — 1°  for  about  720  feet  of  ascent. 
In  the  Alps  the  differences  of  temperature  at  great  heights 
are  accordingly  far  more  considerable,  so  that  upon  the 
higher  parts  of  their  peaks  and  slopes  the  snow  which  has 
fallen  in  winter  no  longer  melts  in  summer.  This  line, 
above  which  snow  covers  the  ground  throughout  the  entire 
year,  is  well  known  as  the  snow-line;  on  the  northern 
side  of  the  Alps  it  is  about  8,000  feet  high,  on  the 
southern  side  about  8,800  feet.  Above  the  snow-line  it 
may  on  sunny  days  be  very  warm  ;  the  unrestrained  radi- 
ation of  the  sun,  increased  by  the  light  reflected  from  the 
snow,  often  becomes  utterly  unbearable ;  so  that  the 
tourist  of  sedentary  habits,  apart  from  the  dazzling  of  his 
eyes,  which  he  must  protect  by  dark  spectacles  or  by  a 
veil,  usually  gets  severely  sunburnt  in  the  face  and  hands, 
the  result  of  which  is  an  inflammatory  swelling  of  thei 
skin  and  great  blisters  on  the  surface.  More  pleasant 
testimonies  to  the  power  of  the  sunshine  are  the  vivid 
colours  and  the  powerful  odour  of  the  small  Alpine  flowers 
which  bloom  in  the  sheltered  rocky  clefts  amoug  the  snow- 
fields.  Notwithstanding  the  powerful  radiation  of  the  sun 
the  temperature  of  the  air  above  the  snow-fields  only  rises 
to  5°,  or  at  most  8°  ;  this,  however,  is  sufficient  to  melt  a 
tolerable  amount  of  the  superficial  layers  of  snow.  But 
the  warm  hours  and  days  are  too  short  to  overpower  the 
great  masses  of  snow  which  have  fallen  during  colder 
times.  Hence  the  height  of  the  snow-line  does  not  de- 
pend merely  on  the  temperature  of  the  mountain  slope, 
but  also  essentially  on  the  amount  of  the  yearly  snow-fall. 
It  is  lower,  for  instance,  on  the  moist  and  warm  south 
slope  of  the  Himalayas,  than  on  the  far  colder  but  also  far 
drier  north  slope  of  the  same  mountain.  Corresponding 
to  the  moist  climate  of  western  Europe,  the  snow-fall 
upon  the  Alps  is  very  great,  and  hence  the  number  and 
extent  of  their  glaciers  are  comparatively  considerable,  so 


ICE   AM)    GLACIERS.  Ill 

that  few  mountains  of  the  earth  can  be  compared  with 
them  in  this  respect.  Such  a  development  of  the  glacial 
world  is,  as  far  as  we  know,  met  with  only  on  the  Hima- 
layas, favoured  by  the  greater  height ;  in  Grreenland  and 
in  I^orthern  Norway,  owing  to  the  colder  climate  ;  in  a 
few  islands  in  Iceland  ;  and  in  New  Zealand,  from  the 
more  abundant  moisture. 

Places  above  the  snow-line  are  thus  characterised  by 
the  fact  that  the  snow  which  in  the  course  of  the  year 
falls  on  its  surface,  does  not  quite  melt  away  in  summer, 
but  remains  to  some  extent.  This  snow,  which  one 
summer  has  left,  is  protected  from  the  further  action 
of  the  sun's  heat  by  the  fresh  quantities  that  fall  upon 
it  during  the  next  autumn,  winter,  and  spring.  Of  this 
new  snow  also  next  summer  leaves  some  remains,  and 
thus  year  by  year  fresh  layers  of  snow  are  accumulated  one 
above  the  other.  In  those  places  where  such  an  accu- 
mulation of  snow  ends  in  a  steep  precipice,  and  its  inner 
structure  is  thereby  exposed,  the  regularly  stratified  yearly 
layers  are  easily  recognised. 

But  it  is  clear  that  this  accumulation  of  layer  upon 
layer  cannot  go  on  indefinitely,  for  otherwise  the  height 
of  the  snow  peak  would  continually  increase  year  by  year. 
But  the  more  the  snow  is  accumulated  the  steeper  are  the 
slopes,  and  the  greater  the  weight  which  presses  upon  the 
lower  and  older  layers  and  tries  to  displace  them.  Ulti- 
mately a  state  must  be  reached  in  which  the  snow  slopes 
are  too  steep  to  allow  fresh  snow  to  rest  upon  them,  and 
in  which  the  burden  which  presses  the  lower  layers  down- 
wards is  so  great  that  these  can  no  longer  retain  their 
position  on  the  sides  of  the  mountain.  Thus,  part  of  the 
snow  which  had  originally  fallen  on  the  higher  regions  of 
the  mountain  above  the  snow-line,  and  had  there  been 
protected  from  melting,  is  compelled  to  leave  its  original 
position  and  seek  a  new  one,  which  it  of  course  finds  only 


112  ICE   A^T)    GLACIERS. 

below  the  snow-line  on  the  lower  slopes  of  the  monntain, 
and  especially  in  the  valleys,  where  however  being  exposed 
to  the  influence  of  a  warmer  air,  it  ultimately  melts  and 
flows  away  as  water.  The  descent  of  masses  of  snow  from 
their  original  positions  sometimes  happens  suddenly  in 
avalanches^  but  it  is  usually  veiy  gradual  in  the  form  of 
glaciers. 

Thus  we  must  discriminate  between  two  distinct  parts  of 
the  ice-fields ;  that  is,  first,  the  snow  which  originally  fell 
— QoXledifirn  in  Switzerland — above  the  snow-line,  cover- 
ing the  slopes  of  the  peaks  as  far  as  it  can  hang  on  to 
them,  and  filling  up  the  upper  wide  kettle-shaped  ends 
of  the  valleys  forming  widely  extended  fields  of  snow  or 
firnmeere.  Secondly,  the  glaciers,  called  in  the  Tyrol 
firner^  which  as  prolongations  of  the  snow-fields  often 
extend  to  a  distance  of  from  4,000  to  5,000  feet  below 
the  snow-line,  and  in  which  the  loose  snow  of  the 
snow-fields  is  again  found  changed  into  transparent  solid 
ice.  Hence  the  name  glacier^  which  is  derived  from  the 
Latin,  glacies  ;  French,  glace,  glacier. 

The  outward  appearance  of  glaciers  is  very  character- 
istically described  by  comparing  them  with  Groethe  to 
currents  of  ice.  They  generally  stretcli  from  the  snow- 
fields  along  the  depth  of  the  valleys,  filling  them  through- 
out their  entire  breadth,  and  often  to  a  considerable 
height.  They  thus  follow  all  the  curvatures,  windings, 
contractions,  and  enlargements  of  the  valley.  Two  glaciers 
frequently  meet,  the  valleys  of  which  unite.  The  two 
glacial  currents  then  join  in  one  common  principal  cur- 
rent, filling  up  the  valley  common  to  them  both.  In 
some  places  these  ice-currents  present  a  tolerably  level  and 
coherent  surface,  but  they  are  usually  traversed  by  cre- 
vasses, and  both  over  the  surface  and  through  the  crevasses 
countless  small  and  large  water  rills  ripple,  which  carry 
off  the  water  formed  by  the  melting  of  the  ice.  United, 
and  forming  a  stream,  they  burst,  through  a  vaulted  and 


ICE  AOT)   GLACIERS. 


113 


clear  blue  gateway  of  ice,  out  at  the  lower  end  of  the 
larger  glacier. 

On  the  surface  of  the  ice  there  is  a  large  quantity  of 
blocks  of  stone,  and  of  rocky  debris,  which  at  the  lower 
end  of  the  glacier  are  heaped  up  and  form  immense  walls  ; 
these  are  called  the  lateral  and  terminal  moraine  of  the 
glacier.  Other  heaps  of  rock,  the  central  moraine,  stretch 
along  the  surface  of  the  glacier  in  the  direction  of  its 

Fm.  13. 


length,  forming  loug  regular  dark  lines.  These  always 
start  from  the  places  where  two  glacier  streams  coincide 
and  unite.  The  central  moraines  are  in  such  places  to  be 
regarded  as  the  continuations  of  the  united  lateral 
moraines  of  the  two  glaciers. 

The  formation  of  the  central  moraine  is  well  represented 
in  the  view  above  given  of  the  Unteraar  Griacier.   Fig.  1 3. 


114  ICE   AXD   GLACIERS. 

In  the  background  are  seen  the  two  glacier  currents 
emerging  from  different  valleys  ;  on  the  right  from  the 
Schreckhorn,  and  on  the  left  from  the  Finsteraarhorn. 
From  the  place  where  they  unite  the  rocky  wall  occupy- 
ing the  middle  of  the  picture  descends,  constituting  the 
central  moraine.  On  the  left  are  seen  individual  large 
masses  of  rock  resting  on  pillars  of  ice,  which  are  known 
as  glacier  tables. 

To  exemplify  these  circumstances  still  further,  I  lay 
before  you  in  Fig-  14  a  map  of  the  Mer  de  Glace  of 
Chamovmi,  copied  from  that  of  Forbes. 

The  3Ier  de  Glace  in  size  is  well  known  as  the  largest 
glacier  in  Switzerland,  although  in  length  it  is  exceeded  by 
the  Aletsch  Glacier.  It  is  formed  from  the  snow-fields  that 
cover  the  heights  directly  north  of  Mont  Blanc,  several  of 
which,  as  the  Grande  Jorasse,  the  Aiguille  Verte  (a, 
Figs.  14  and  15),  the  Aiguille  du  Geant  (b),  Aiguille  du 
Midi  (c),  and  the  Aiguille  du  Dru  (d),  are  only  2,000  to 
3,000  feet  below  that  king  of  the  European  mountains. 
The  snow-fields  which  lie  on  the  slopes  and  in  the  basins 
between  these  mountains  collect  in  three  principal  cur- 
rents, the  Glacier  du  Geant,  Glacier  de  Lechaud,  and 
Glacier  du  Talefre,  which,  ultimately  united  as  represented 
in  the  map,  form  the  Mer  de  Glace  ;  this  stretches  as  an 
ice  current  2,600  to  3,000  feet  in  breadth  down  into  the 
valley  of  Chamouni,  where  a  powerful  stream,  the  Arvey- 
ron,  bursts  from  its  lower  end  at  k,  and  plunges  into  the 
Arve.  The  lowest  precipice  of  the  Mer  de  Glace,  wliich 
is  visible  from  the  valley  of  Chamouni,  and  forms  a  large 
cascade  of  ice,  is  commonly  called  Glacier  des  Bois,  from 
a  small  village  which  lies  below. 

Most  of  the  visitors  at  Chamouni  only  set  foot  on  the 
lowest  part  of  the  Mer  de  Glace  from  the  inn  at  the 
Montanvert,  and  when  they  are  free  from  giddiness  cross 
the  glacier  at  this  place  to  the  little  house  on  the  oppo- 


ICE   AND   GLACIERS. 


115 


site  side,  the  Clmpeau  (n).  Although,  as  the  map  shows, 
only  a  comparatively  very  small  portion  of  the  glacier  is 
thus  seen  and  crossed,  this   way  shows  sufficiently  the 


Fia  14. 

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<^A 


'^Mmm?^ 


^v 


^4% 
«?^, 


»« •tf^'^  -»i«if^  *sn**~-c^  ^   '^  4e     wM  ^^  "       ^ 


.msvWf  *,    ■     'SMS.  \/    .' 


magnificent  scenes,  and  also  the  difficulties  of  a  glacier 
excursion.  Bolder  wanderers  march  upwards  along  the 
glacier  to  the   Jardin,  a  rocky  cliff  clothed  with  some 


IIG  ICE   AND   GLACIERS. 

vegetation,  which  divides  the  glacial  current  of  the  Gla- 
cier du  Talefre  into  two  branches ;  and  bolder  still  they 
ascend  yet  higher,  to  the  Col  du  Geant  (11,000  feet  above 
the  sea),  and  down  the  Italian  side  to  the  valley  of  Aosta. 

The  surface  of  the  Mer  de  Glace  shows  four  of  the 
rocky  walls  which  we  have  designated  as  medial  moraines. 
The  first,  nearest  the  east  side  of  the  glacier,  is  formed 
where  the  two  arms  of  the  Glacier  du  Talefre  unite  at  the 
lower  end  of  the  Jardin  ;  the  second  proceeds  from  the 
union  of  the  glacier  in  question  with  the  Glacier  de 
Lechaud ;  the  third,  from  the  union  of  the  last  with  the 
Glacier  du  Geant ;  and  the  fourth,  finally,  from  the  top  of 
the  rock  ledge  which  stretches  from  the  Aiguille  du 
Geant  towards  the  cascade  (g)  of  the  Glacier  du  Geant. 

To  give  you  an  idea  of  the  slope  and  the  fall  of  the 
glacier,  I  have  given  in  Fig.  15  a  longitudinal  section  of 
it  according  to  the  levels  and  measurements  taken  by 
Forbes,  with  the  view  of  the  right  bank  of  the  glacier. 
The  letters  stand  for  the  same  objects  as  in  Fig.  14  ;  p  is 
the  Aiguille  de  Lechaud,  q  the  Aiguille  Noire,  r  the 
Mont  Tacul,  f  is  the  Col  du  Geant,  the  lowest  point  in 
the  high  wall  of  rock  that  surrounds  the  upper  end  of 
the  snow-fields  which  feed  the  Mer  de  Glace.  The  base 
line  corresponds  to  a  length  of  a  little  more  than  nine 
miles :  on  the  right  the  heights  above  the  sea  are  given  in 
feet.  The  drawing  shows  very  distinctly  how  small  in 
most  places  is  the  fall  of  the  glacier.  Only  an  approxi- 
mate estimate  could  be  made  of  the  depth,  for  hitherto 
nothing  certain  has  been  made  out  in  reference  to  it.  But 
that  it  is  very  deep  is  obvious  from  the  following  indivi- 
dual and  accidental  observations. 

At  the  end  of  a  vertical  rock  wall  of  the  Tacul,  tlie 
edge  of  the  Glacier  du  Geant  is  pushed  forth,  forming  an 
ice  wall  140  feet  in  height.  This  would  give  the  depth 
of  one  of  the  upper  arms  of  the  glacier  at  the  edge.     In 


ICE   AND   GLACIERS. 


117 


the  middle  and  after  the  union 
of  the  three  glaciers  the  depth 
must  be  far  greater.  Somewhat 
below  the  junction  Tyndall  and 
Hirst  sounded  a  moulin,  that  is 
a  cavity  through  which  the  sur- 
face glacier  waters  escape,  to  a 
depth  of  160  feet;  the  guides 
alleged  that  they  had  sounded 
a  similar  aperture  to  a  depth 
of  350  feet,  and  had  found  no 
bottom.  From  the  usually  deep 
trough  shaped  or  gorge-like  form 
of  the  bottom  of  the  valleys, 
which  is  constructed  solely  of 
rock  walls,  it  seems  improbable 
that  for  a  breadth  of  3,000  feet 
the  mean  depth  should  only  be 
350  feet ;  moreover,  from  the 
manner  in  which  ice  moves,  there 
must  necessarily  be  a  very  thick 
coherent  mass  beneath  the  cre- 
vassed  part. 

To  render  these  magnitudes 
more  intelligible  by  reference  to 
more  familiar  objects,  imagine 
the  valley  of  Heidelberg  filled 
with  ice  up  to  the  Molkencur, 
or  higher,  so  that  the  whole 
town,  with  all  its  steeples  and 
the  castle,  is  buried  deeply 
beneath  it ;  if,  further,  you  ima- 
gine this  mass  of  ice,  gradually 
extending  in  height,  continued 
from  the  mouth  of  the  valley  up 
to  Neckargemiind,  that  would 
about  correspond  to  the   lower 


>^\^V^> 


^i^-   - 


%■  \  .  \  L- 


118 


ICE   ASJ)    GLACIERS. 


united  ice  cun-ent  of  the  Mer  de  Glace.  Or,  instead 
of  the  Ehine  and  the  Nahe  at  13ingen,  suppose  two  ice 
currents  uniting  which  fill  the  Rhine  valley  to  its  upper 
border  as  far  as  we  can  see  from  the  river,  and  then  the 
united  currents  stretching  downwards  to  beyond  Asmann- 
shausen  and  Burg  Eheinstein  ;  such  a  current  would  also 
about  correspond  to  the  size  of  the  Mer  de  Griace. 

Fig.  16,  which  is  a  view  of  the  magnificent  Gorner 

Fig.  16. 


u  lacier  seen  from  below,  also  gives  an  idea  of  the  size  of 
the  masses  of  ice  of  the  larger  glaciers. 

The  surface  of  most  glaciers  is  dirty,  from  the  numerous 
pebbles  and  sand  which  lie  upon  it,  and  which  are  heaped 
together  the  more  the  ice  under  them  and  among  them 
melts  away.  The  ice  of  the  surface  has  been  partially 
destroyed  and  rendered  crumbly.  In  the  depths  of  the 
crevasses  ice  is  seen  of  a  purity  and  clearness  with  which 


ICE  AKT)   GLACIERS,  119 

nothing  that  we  are  acquainted  with  on  the  plains  can  be 
compared.      From  its  purity  it  shows  a  splendid  blue, 
like  that  of  the  sky,  only  with  a  greenish  hue.   Crevasses  in 
which  pure  ice  is  visible  in  the  interior  occur  of  all  sizes  ; 
in  the  beginning  they  form  slight  cracks  in  which  a  knife 
can  scarcely  be  inserted  ;    becoming  gradually  enlarged  to 
chasms,  hundreds,  or  even  thousands,  of  feet  in  length, 
and  twenty,  fifty,   and  as  much  as  a  hundred   feet  in 
breadth,  while  some    of  them   are   immeasurably  deep. 
Their  vertical  dark  blue  walls  of  crystal  ice,  glistening 
with  moisture  from  the  trickling  water,  form  one  of  the 
most  splendid  spectacles  which  nature  can  present  to  us ; 
but,  at  the  same  time,  a  spectacle  strongly  impregnated 
with  the  excitement  of  danger,  and  only  enjoyable  by  the 
traveller  who  feels  perfectly  free  from  the  slightest  ten- 
dency to  giddiness.     The  tourist  must  know  how,  with 
the  aid  of  well-nailed  shoes  and  a  pointed  Alpenstock,  to 
stand  even  on  slippery  ice,  and  at  the  edge  of  a  vertical 
precipice  the  foot  of  which  is  lost  in  the  darkness  of 
night,  and  at  an  unknown  depth.     Such  crevasses  cannot 
always  be  evaded  in   crossing  the  glacier;  at  the  lower 
part  of  the  Mer  de  Glace,  for  instance,  where  it  is  usually 
crossed  by  travellers,  we  are  compelled  to  travel  along 
some  extent  of  precipitous  banks  of  ice,  which  are  oc- 
casionally only    four    to    six   feet   in    breadth,   and    on 
each    side    of    which   is    such   a   blue    abyss.      Many   a 
traveller,  who    has   crept  along   the   steep  rocky  slopes 
without  fear,  there  feels  his  heart  sink,  and  cannot  turn 
his  eyes  from  the  yawning  chasm,  for  he  must  first  care- 
fully select  every  step  for  his  feet.     And  yet  these  blue 
chasms,  which  lie  open  and  exposed  in  the  daylight,  are 
by  no  means  the  worst  dangers  of  tlie  glacier ;    though 
indeed  we  are  so  organised  that  a  danger  which  we  per- 
ceive, and  which  therefore  we  can  safely  avoid,  frightens  us 
far  more  than  one  which   we  know  to  exist,  but  which 


120  ICE   AND   GLACIERS. 

is  veiled  from  our  eyes.  So  also  it  is  with  glacier 
chasms.  In  the  lower  part  of  the  glacier  they  yawn 
before  us,  threatening  death  and  destruction,  and  lead  us, 
timidly  collecting  all  our  presence  of  mind,  to  shrink  from 
them  ;  thus  accidents  seldom  occur.  On  the  upper  part 
of  the  glacier,  on  the  contrary,  the  surface  is  covered  with 
snow ;  this,  when  it  falls  thickly,  soon  arches  over  the 
narrower  crevasses  of  a  breadth  of  from  four  to  eight  feet, 
and  forms  bridges  which  quite  conceal  the  crevasse,  so  that 
the  traveller  only  sees  a  beautiful  plane  snow  surface 
before  him.  If  the  snow  bridges  are  thick  enough,  they 
will  support  a  man ;  but  they  are  not  always  so,  and  these 
are  the  places  where  men,  and  even  chamois,  are  so  often 
lost.  These  dangers  may  readily  be  guarded  against  if 
two  or  three  men  are  roped  together  at  intervals  of  ten 
or  twelve  feet.  If  then  one  of  them  falls  into  a  crevasse, 
the  two  others  can  hold  him,  and  draw  him  out  again. 

In  some  places  the  crevasses  may  be  entered,  especially 
at  the  lower  end  of  a  glacier.  In  the  well-known  glaciers 
of  Grrindelwald,  Eosenlaui,  and  other  places,  this  is  facili- 
tated by  cutting  steps  and  arranging  wooden  planks. 
Then  anyone  who  does  not  fear  the  perpetually  trickling 
water  may  explore  these  crevasses,  and  admire  the  won- 
derfully transparent  and  pure  crystal  walls  of  these 
caverns.  The  beautiful  blue  colour  which  they  exhibit 
is  the  natural  colour  of  perfectly  pure  water ;  liquid 
water  as  well  as  ice  is  blue,  though  to  an  extremely  small 
extent,  so  that  the  colour  is  only  visible  in  layers  of  from 
ten  to  twelve  feet  in  thickness.  The  water  of  the  Lake  of 
Geneva  and  of  theLago  di  Garda  exhibits  the  same  splendid 
colour  as  ice. 

The  glaciers  are  not  everywhere  crevassed  ;  in  places 
where  the  ice  meets  with  an  obstacle,  and  in  the  middle 
of  great  glacier  currents  the  motion  of  which  is  uniform, 
the  surface  is  perfectly  coherent. 


ICE   AND    GLACIERS. 


121 


Fig.  17  represents  one  of  the  more  level  parts  of  the 
Mer  de  Glace  at  the  Montanvert,  the  little  house  of 
which  is  seen  in  the  background.  The  Gries  Glacier, 
where  it  forms  the  height  of  the  pass  from  the  Upper 
Ehone  valley  to  the  Tosa  valley,  may  even  be  crossed  on 

Fig.  17. 


horseback.  We  find  the  greatest  disturbance  of  the 
surface  of  the  glacier  in  those  places  where  it  passes 
from  a  slightly  inclined  part  of  its  bed  to  one  where  the 
slope  is  steeper.  The  ice  is  there  torn  in  all  directions 
into  a  quantity  of  detached  blocks,  which  by  melting 


122  ICE   AND   GLACIERS. 

are  usually  changed  into  wonderfully  shaped  sharp  ridges 
and  pyramids,  and  from  time  to  time  fall  into  the  inter- 
jacent crevasses  with  a  loud  rumbling  noise.  Seen  from  a 
distance  such  a  place  appears  like  a  wild  frozen  waterfall, 
and  is  therefore  called  a  cascade  ;  such  a  cascade  is  seen  in 
the  Glacier  du  Talefre  at  1,  another  is  seen  in  the  Glacier 
du  Geant  at  g,  Fig.  14,  while  a  third  forms  the  lower  end 
of  the  Mer  de  Glace.  The  latter,  already  mentioned  as 
the  Glacier  des  Bois,  which  rises  directly  from  the  trough 
of  the  valley  at  Chamouni  to  a  height  of  1,700  feet,  the 
height  of  the  Konigstuhl  at  Heidelberg,  affords  at  all 
times  a  chief  object  of  admiration  to  the  Chamouni  tourist. 
Fig.  18  represents  a  view  of  its  fantastically  rent  blocks 
of  ice. 

We  have  hitherto  compared  the  glacier  with  a  current 
as  regards  its  outer  form  and  appearance.  This  similarity, 
however,  is  not  merely  an  external  one :  the  ice  of  the 
glacier  does,  indeed,  move  forwards  like  the  water  of  a 
stream,  only  more  slowly.  That  this  must  be  the  case 
follows  from  the  considerations  by  which  I  have  en- 
deavoured to  explain  the  origin  of  a  glacier.  For  as  the 
ice  is  being  constantly  diminished  at  the  lower  end  by 
melting,  it  would  entirely  disappear  if  fresh  ice  did  not 
continually  press  forward  from  above,  which,  again,  is 
made  up  by  the  snowfalls  on  the  mountain  tops. 

But  by  careful  ocular  observation  we  may  convince 
ourselves  that  the  glacier  does  actually  move.  For  the 
inhabitants  of  the  valleys,  who  have  the  glaciers  constantly 
before  their  eyes,  often  cross  them,  and  in  so  doing  make 
use  of  the  larger  blocks  of  stone  as  sign  posts — detect 
this  motion  by  the  fact  that  their  guide  posts  gradually 
descend  in  tlie  course  of  each  year.  And  as  the  yearly 
displacement  of  the  lower  half  of  the  Mer  de  Glace  at 
Chamouni  amounts  to  no  less  than  from  400  to  600  feet, 
you  can  readily  conceive  that  such  displacements  must 


ICE   AND    GLACIERS. 


123 


ultimately  be  observed,  notwithstanding  the  slow  rate  at 
which  they  take  place,  and  in  spite  of  the  chaotic  confu- 
sion of  crevasses  and  rocks  which  the  glacier  exhibits. 

Besides  rocks   and   stones,  other   objects   which    have 
accidentally  alighted  upon  the  glacier  are  dragged  along. 

Fig.  18. 


In  1788  the  celebrated  Genevese  Saussure,  together  with 
his  son  and  a  company  of  guides  and  porters,  spent 
sixteen  days  on  the  Col  du  Greant.  On  descending  the  rocks 
at  the  side  of  the  cascade  of  the  Glacier  du  Geant,  they 


124 


ICE   AND    GLACIERS. 


left  behind  them  a  wooden  ladder.  This  was  at  the 
foot  of  the  Aiguille  Noire,  where  the  fourth  band  of  the  Mer 
de  Glace  begins  ;  this  line  thus  marks  at  the  same  time 
the  direction  in  which  ice  travels  from  this  point.  In  the 
year  1832,  that  is,  forty-four  years  after,  fragments  of 
this  ladder  were  found  by  Forbes  and  other  travellers 
not  far  below  the  junction  of  the  three  glaciers  of  the 
Mer  de  Glace,  in  the  same  line  (at  s.  Fig.    19),   from 

Tig.  19. 


^Miidik 


which  it  results  that  these  parts   of    the  glacier  must 
on  the  average  have  each  year  descended  375  feet. 

In  the  year  1827  Hugi  had  built  a  Imt  on  the  central 
moraine  of  the  Unteraar  Glacier  for  the  purpose  of 
making  observations ;  the  exact  position  of  this  hut  was 


ICE   AND    GLACIERS.  125 

determined  by  himself  and  afterwards  by  Agassiz,  and 
they  found  that  each  year  it  had  moved  downwards. 
Fourteen  years  later,  in  the  year  1841,  it  was  4,884  feet 
lower,  so  that  every  year  it  had  on  the  average  moved 
through  349  feet.  Agassiz  afterwards  found  that  his 
own  hut,  which  he  had  erected  on  the  same  glacier,  had 
moved  to  a  somewhat  smaller  extent.  For  these  observa- 
tions a  long  time  was  necessary.  But  if  the  motion 
of  the  glacier  be  observed  by  means  of  accurate  measuring 
instruments,  such  as  theodolites,  it  is  not  necessary  to 
wait  for  years  to  observe  that  ice  moves — a  single  day 
is  sufficient. 

Such  observations  have  in  recent  times  been  made 
by  several  observers,  especially  by  Forbes  and  by  Tyn- 
dall.  They  show  that  in  summer  the  middle  of  the 
Mer  de  Glace  moves  through  twenty  inches  a  da,y,  while 
towards  the  lower  terminal  cascade  the  motion  amounts 
to  as  much  as  thirty-five  inches  in  a  day.  In  winter  the 
velocity  is  only  about  half  as  great.  At  the  edges  and 
in  the  lower  layers  of  the  glacier,  as  in  a  flow  of  water, 
it  is  considerably  smaller  than  in  the  centre  of  the  sur- 
face. 

The  upper  sources  of  the  Mer  de  Grlace  also  have 
a  slower  motion,  the  Glacier  du  Geant  thirteen  inches 
a  day,  and  the  Glacier  du  Lechaud  nine  inches  and  a 
half.  In  different  glaciers  the  velocity  is  in  general 
very  various,  according  to  the  size,  the  inclination,  the 
amount  of  snow-fall,  and  other  circumstances. 

Such  an  enormous  mass  of  ice  thus  gradually  and 
gently  moves  on,  imperceptibly  to  the  casual  observer, 
about  an  inch  an  hour — the  ice  of  the  Col  du  Geant 
will  take  120  years  before  it  reaches  the  lower  end 
of  the  Mer  de  Glace — but  it  moves  forward  with  un- 
controllable force,  before  which  any  obstacles  that  man 
could   oppose   to   it   yield   like   straws,   and   the   traces 


126  ICE  AXD    GLACIERS. 

of  which  are  distinctly  seen  even  on  the  granite  walls 
of  the  valley.  If,  after  a  series  of  wet  seasons,  and 
an  abundant  fall  of  snow  on  the  heights,  the  base  of 
a  glacier  advances,  not  merely  does  it  crush  dwelling 
houses,  and  break  the  trunks  of  powerful  trees,  but  the 
glacier  pushes  before  it  the  boulder  walls  which  form 
its  terminal  moraine  without  seeming  to  experience  any 
resistance.  A  truly  magnificent  spectacle  is  this  motion, 
so  gentle,  and  so  continuous,  and  yet  so  powerful  and  so 
irresistible. 

I  will  mention  here  that  from  the  way  in  which  the 
glacier  moves  we  can  easily  infer  in  what  places  and 
in  what  directions  crevasses  will  be  formed.  For  as 
all  layers  of  the  glacier  do  not  advance  with  equal 
velocity,  some  points  remain  behind  others  :  for  instance, 
the  edges  as  compared  with  the  middle.  Thus  if  we 
observe  the  distance  from  a  given  point  at  the  edge 
to  a  given  point  of  the  middle,  both  of  which  were 
originally  in  the  same  line,  but  the  latter  of  which 
afterwards  descended  more  rapidly,  we  shall  find  that 
this  distance  continually  increases ;  and  since  the  ice 
cannot  expand  to  an  ex'tent  corresponding  to  the  in- 
creasing distance,  it  breaks  up  and  forms  crevasses, 
as  seen  along  the  edge  of  the  glacier  in  Fig,  20,  which 
represents  the  Grorner  Glacier  at  Zermatt.  It  would 
lead  me  too  far  if  I  were  here  to  attempt  to  give  a 
detailed  explanation  of  the  formation  of  the  more  regular 
system  of  crevasses,  as  they  occur  in  certain  parts  of  all 
glaciers  ;  it  may  be  sufficient  to  mention  that  the  con- 
clusions deducible  from  the  considerations  above  stated 
are  fully  borne  out  by  observation. 

I  will  only  draw  attention  to  one  point — what  extremely 
small  displacements  are  sufficient  to  cause  ice  to  form 
hiuidreds  of  crevasses.  The  section  of  the  Mer  de  Glace 
(P'ig.    21,   at   g,  c,  h)   shows   places   where   a   scarcely 


ICE   AND   GLACIERS. 


127 


perceptible  cliange  in  the  inclination  of  the  surface  of 
the  ice  occurs  of  from  two  to  four  degrees.  This  is 
sufficient  to  produce  a  system  of  cross  crevasses  on  the 
surface.  Tyndall  more  especially  has  urged  and  con- 
firmed by  observation  and  measurements,  that  the  mass 
of  ice  of  the  glacier  does  not  give  way  in  the  smallest 

Fig.  20. 


degree   to    extension,  but  when   subjected   to  a  pull  is 
invariably  torn  asunder. 

The  distribution  of  the  boulders,  too,  on  the  surface 
of  the  glacier  is  readily  explained  when  we  take  their 
motion  into  account.  These  boulders  are  fragments  of 
the  mountains  between  which  the  glacier  flows.   Detached 


128 


ICE  AND   GLACIERS. 


Fig.  21. 


n 


partly  by  the   weathering    of 
the  stone,  and  partly  by  the 
^  ^ezing  of  water  in  its  crevices, 
1 1  ey  fall,  and  for  the  most  part 
the  edge  of  the  mass  of  ice. 
1  Iiere  they  either  remain   ly- 
y  on  the  surface,  or  if  they 
1    ve    originally   burrowed    in 
i  1  3  snow,  they  ultimately  re- 
j  pear  in  consequence  of  the 
1    siting     of    the     superficial 
1    ^ers   of  ice  and  snow,    and 
tl  sy     accumulate      especially 
t   the  lower  end  of  the    gla- 
sr,  where    more  of  the    ice 
I    tween      them     has       been 
I    ilted.    The  blocks  which  are 
idually  borne  down  to  the 
I    vei  end  of  the  glacier  are 
netimes   quite    colossal    in 
1  e.     Solid    rocky  masses    of 
s  kind  are  met  with  in  the 
1  iteral  and  terminal  moraines, 
^\]lich  are  as  large  as  a  two- 
storied  house. 

The  masses  of  stone  move  in 
hues  which  are  always  nearly 
])  "I  rail  el  to  each  other  and  to 
tli(j  longitudinal  direction  of 
lh(!  glacier.  Those,  therefore, 
th  it  are  already  in  the  middle 
i(  main  in  the  middle,  and 
those  that  lie  on  the  eda'e  re- 
main  at  the  edge.  These  latter 
are  the  more  numerous,  for 
during  the  entire  course  of  the 
glacier,  fresh  boulders  are  con- 


11 


ICE   AND   GLACIERS.  129 

stantly  falling  on  the  edge,  but  cannot  fall  on  the  middle. 
Thus  are  formed  on  the  edge  of  the  mass  of  ice  the  lateral 
moraines,  the  boulders  of  which  partly  move  along  with 
the  ice,  partly  glide  over  its  surface,  and  partly  rest  on 
the  solid  rocky  base  near  the  ice.  But  when  two  glacier 
streams  unite,  their  coinciding  lateral  moraines  come  to 
lie  upon  the  centre  of  the  united  ice-stream,  and  then 
move  forward  as  central  moraines  parallel  to  each  other 
and  to  the  banks  of  the  stream,  and  they  show,  as  far 
as  the  lower  end,  the  boundary-line  of  the  ice  which 
originally  belonged  to  one  or  the  other  of  the  arms  of  the 
glacier.  They  are  veiy  remarkable  as  displaying  in  what 
regular  parallel  bands  the  adjacent  parts  of  the  ice-stream 
glide  downwards.  A  glance  at  the  map  of  the  Mer  de 
Grlace,  and  its  four  central  moraines,  exhibits  this  very 
distinctly. 

On  the  Glacier  du  Geant  and  its  continuation  in  the 
Mer  de  Glace,  the  stones  on  the  surface  of  the  ice 
delineate,  in  alternately  grayer  and  whiter  bands,  a  kind 
of  yearly  rings  which  were  first  observed  by  Forbes. 
For  since  in  the  cascade  at  g.  Fig.  21,  more  ice  slides 
down  in  summer  than  in  winter,  the  surface  of  the 
ice  below  the  cascade  forms  a  series  of  terraces  as  seen 
in  the  drawing,  and  as  those  slopes  of  the  terraces  which 
have  a  northern  aspect  melt  less  than  their  upper  plane 
surfaces,  the  former  exhibit  purer  ice  than  the  latter. 
This,  according  to  Tyndall,  is  the  probable  origin  of 
these  dirt  bands.  At  first  they  run  pretty  much  across 
the  glacier,  but  as  afterwards  their  centre  moves  some- 
what more  rapidly  than  the  ends,  they  acquire  farther 
down  a  curved  shape,  as  represented  in  the  map,  Fig.  19. 
By  their  curvature  they  thus  show  to  the  observer  with 
what  varying  velocity  ice  advances  in  the  different  parts 
of  its  course. 

A  very  peculiar  part  is  played  by  certain  stones  which 


130  ICE   AXD    GLACIERS. 

are  imbedded  in  the  lower  surface  of  the  mass  of  ice,  and 
which  have  partly  fallen  there  through  crevasses,  and 
may  partly  have  been  detached  from  the  bottom  of  the 
valley.  For  these  stones  are  gradually  pushed  with  the 
ice  along  the  base  of  the  valley,  and  at  the  same  time  are 
pressed  against  this  base  by  the  enormous  weight  of  the 
superincumbent  ice.  Both,  the  stones  imbedded  in  the 
ice,  as  well  as  the  rocky  base,  are  equally  hard,  but  by 
their  friction  against  each  other  they  are  ground  to 
powder  with  a  power  compared  to  which  any  human 
exertion  of  force  is  infinitely  small.  The  product  of 
this  friction  is  an  extremely  fine  powder  which,  swept 
away  by  water,  appears  lower  down  in  the  glacier  brook, 
imparting  to  it  a  whitish  or  yellowish  muddy  appearance. 

The  rocks  of  the  trough  of  the  valley,  on  the  contrary, 
on  which  the  glacier  exerts  year  by  year  its  grinding 
power,  are  polished  as  if  in  an  enormous  polishing 
machine.  They  remain  as  rounded,  smoothly  polished 
masses,  in  which  are  occasional  scratches  produced  by 
individual  harder  stones.  Thus  we  see  them  appear  at 
the  edge  of  existing  glaciers,  when  after  a  series  of  dry 
and  hot  seasons  the  glaciers  have  somewhat  receded. 
But  we  find  such  polished  rocks  as  remains  of  gigantic 
ancient  glaciers  to  a  far  greater  extent  in  the  lower 
parts  of  many  Alpine  valleys.  In  the  valley  of  the  Aar 
more  especially,  as  far  down  as  Meyringen,  the  rock- walls 
polished  to  a  considerable  height  are  very  characteristic. 
There  also  we  find  the  celebrated  polished  plates,  over 
wliich  the  way  passes,  and  which  are  so  smooth  that 
furrows  have  had  to  be  hewn  into  them  and  rails  erected 
to  enable  men  and  animals  to  traverse  them  in  safety. 

The  former  enormous  extent  of  glaciers  is  recognised 
by  ancient  moraine-dykes,  and  by  transported  blocks  of 
stone,  as  well  as  by  these  polished  rocks.  The  blocks  of 
stone  which  have  been  carried  away  by  the  glacier  are 


ICE   AND    GLACIERS.  131 

distinguished  from  those  which  water  has  rolled  down, 
by  their  enormous  magnitude,  by  the  perfect  retention 
of  all  their  edges  which  are  not  at  all  rounded  off,  and 
finally  by  their  being  deposited  on  tlie  glacier  in  exactly 
the  same  order  in  which  the  rocks  of  which  they  formed 
part  stand  in  the  mountain  ridge  ;  while  the  stones 
which  currents  of  water  carry  along  are  completely 
mixed  together. 

From  these  indications,  geologists  have  been  able  to 
prove  that  the  glaciers  of  Chamouni,  of  Monte  Eosa, 
of  the  St.  Grotthard,  and  the  Bernese  Alps,  formerly 
penetrated  through  the  valley  of  the  Arve,  the  Rhone, 
the  Aare,  and  the  Ehine  to  the  more  level  part  of 
Switzerland  and  the  Jura,  where  they  have  deposited 
their  boulders  at  a  height  of  more  than  a  thousand  feet 
above  the  present  level  of  the  Lake  of  Neufchatel. 
Similar  traces  of  ancient  glaciers  are  found  upon  the 
mountains  of  the  British  Islands,  and  upon  the  Scan- 
dinavian Peninsula. 

The  drift-ice  too  of  the  Arctic  Sea  is  glacier  ice ;  it 
is  pushed  down  into  the  sea  by  the  glaciers  of  Grreenland, 
becomes  detached  from  the  rest  of  the  glacier,  and  floats 
away.  In  Switzerland  we  find  a  similar  formation  of 
drift-ice,  though  on  a  far  smaller  scale,  in  the  little 
Marjelen  See,  into  which  part  of  the  ice  of  the  great 
Aletsch  Glacier  pushes  down.  Blocks  of  stone  which  lie 
in  drift-ice  may  make  long  voyages  over  the  sea.  The  vast 
number  of  blocks  of  granite  which  are  scattered  on  the 
North  G-erman  plains,  and  whose  granite  belongs  to  the 
Scandinavian  mountains,  has  been  transported  by  drift- 
ice  at  the  time  when  the  European  glaciers  had  such  an 
enormous  extent. 

I  must  unfortunately  content  myself  with  these  few 
references  to  the  ancient  history  of  glaciers,  and  re- 
vert now  to  the  processes  at  present  at  work  in  them. 

7 


132  ICE   A^^D    GLACIERS. 

From  the  facts  which  I  have  brought  before  you  it 
results  that  the  ice  of  a  glacier  flows  slowly  like  the 
current  of  a  very  viscous  substance,  such  for  instance 
as  honey,  tar,  or  thick  magma  of  clay.  The  mass  of 
ice  does  not  merely  flow  along  the  ground  like  a  solid 
which  glides  over  a  precipice,  but  it  bends  and  twists  in 
itself ;  and  although  even  while  doing  this  it  moves  along 
the  base  of  the  valley,  yet  the  parts  which  are  in  contact 
with  the  bottom  and  the  sides  of  the  valley  are  per- 
ceptibly retarded  by  the  powerful  friction  ;  the  middle 
of  the  surface  of  the  glacier,  which  is  most  distant  both 
from  the  bottom  and  the  sides,  moving  most  rapidly. 
Eendu,  a  Savoyard  priest,  and  the  celebrated  natural 
philosopher  Forbes,  were  the  first  to  suggest  the  similarity 
of  a  glacier  with  a  current  of  a  viscous  substance. 

Now  you  will  perhaps  enquire  with  astonishment  how 
it  is  possible  that  ice,  which  is  the  most  brittle  and 
fragile  of  substances,  can  flow  in  the  glacier  like  a 
viscous  mass ;  and  you  may  perhaps  be  disposed  to 
regard  this  as  one  of  the  wildest  and  most  improbable 
statements  that  have  ever  been  made  by  philosophers. 
I  will  at  once  admit  that  philosophers  themselves  were 
not  a  little  perplexed  by  these  results  of  their  investiga- 
tions. But  the  facts  were  there,  and  could  not  be  got 
rid  of.  How  this  mode  of  motion  originated  was  for  a 
long  time  quite  enigmatical,  the  more  so  since  the 
numerous  crevasses  in  glaciers  were  a  sufficient  indication 
of  the  well-known  brittleness  of  ice;  and  as  Tyndall 
correctly  remarked,  this  constituted  an  essential  diff*erence 
between  a  stream  of  ice  and  the  flow  of  lava,  of  tar,  of 
honey,  or  of  a  current  of  mud. 

The  solution  of  this  strange  problem  was  found,  as  is 
so  often  the  case  in  the  natural  sciences,  in  apparently 
recondite  investigations  into  the  nature  of  heat,  which 
form  one   of  the   most  important  conquests   of  modern 


ICE   AND    GLACIERS.  133 

physics,  and  which  constitute  what  is  known  as  the 
mechanical  theory  of  heat.  Among  a  great  number  of 
deductions  as  to  the  relations  of  the  diverse  natural 
forces  to  each  other,  the  principles  of  the  mechanical 
theory  of  heat  lead  to  certain  conclusions  as  to  the 
dependence  of  the  freezing-point  of  water  on  the  pressure 
to  which  ice  and  water  are  exposed. 

Everyone  knows  that  we  determine  that  one  fixed 
point  of  our  thermometer  scale  which  we  call  the  freez- 
ing-point or  zero,  by  placing  the  thermometer  in  a 
mixture  of  pure  water  and  ice.  Water,  at  any  rate 
when  in  contact  with  ice,  cannot  be  cooled  below  zero 
without  itself  being  converted  into  ice;  ice  cannot  be 
heated  above  the  freezing-point  without  melting.  Ice 
and  water  can  exist  in  each  other's  presence  at  only  one 
temperature,  the  temperature  of  zero. 

Now,  if  we  attempt  to  heat  such  a  mixture  by  a  flame 
beneath  it,  the  ice  melts,  but  the  temperature  of  the 
mixture  is  never  raised  above  that  of  0°  so  long  as  some 
of  the  ice  remains  unmelted.  The  heat  imparted  changes 
ice  at  zero  into  water  at  zero,  but  the  thermometer  in- 
dicates no  increase  of  temperature.  Hence  physici^s 
say  that  heat  has  become  latent,  and  that  water  contains 
a  certain  quantity  of  latent  heat  beyond  that  of  ice  at 
the  same  temperature. 

On  the  other  hand,  when  we  withdraw  more  heat  from 
the  mixture  of  ice  and  water,  the  water  gradually  freezes ; 
but  as  long  as  there  is  still  liquid  water,  the  temperature 
remains  at  zero.  Water  at  0°  has  given  up  its  latent 
heat,  and  has  become  changed  into  ice  at  0°. 

Now  a  glacier  is  a  mass  of  ice  which  is  everywhere 
interpenetrated  by  water,  and  its  internal  temperature 
is  therefore  everywhere  that  of  the  freezing-point.  The 
deeper  layers,  even  of  the  fields  of  neve,  appear  on  the 
heights  which  occur  in  our  Alpine  chain  to  have  every- 


134  ICE   AXD   GLACIERS. 

where  the  same  temperature.  For,  though  the  freshly- 
fallen  snow  of  these  heights  is,  for  the  most  part,  at  a 
lower  temperature  than  that  of  0°,  the  first  hours  of 
warm  sunshine  melt  its  surface  and  form  water,  which 
trickles  into  the  deeper  colder  layers,  and  there  freezes, 
until  it  has  throughout  been  brought  to  the  temperature 
of  the  freezing-point.  This  temperature  then  remains 
unchanged.  P'or,  though  by  the  sun's  rays  the  surface 
of  the  ice  may  be  melted,  it  cannot  be  raised  above  zero, 
and  the  cold  of  winter  penetrates  as  little  into  the  badly- 
conducting  masses  of  snow  and  ice  as  it  does  into  our 
cellars.  Thus  the  interior  of  the  masses  of  neve,  as  well  as 
of  the  glacier,  remains  permanently  at  the  melting-point. 

But  the  temperature  at  which  water  freezes  may  be 
altered  by  strong  pressure.  This  was  first  deduced  from 
the  mechanical  theory  of  heat  by  James  Thomson  of 
Belfast,  and  almost  simultaneously  by  Clausius  of  Zurich  ; 
and,  indeed,  the  amount  of  this  change  may  be  correctly 
predicted  from  the  same  reasoning.  For  each  increase 
of  a  pressure  of  one  atmosphere  the  freezing  point  is 
lowered  by  the  -j-lj-th  part  of  a  degree  Centigrade.  The 
brother  of  the  former.  Sir  W.  Thomson,  the  celebrated 
Glasgow  physicist,  made  an  experimental  confirmation 
of  this  theoretical  deduction  by  compressing  in  a  suit- 
able vessel  a  mixture  of  ice  and  snow.  This  mixture 
became  colder  and  colder  as  the  pressure  was  increased, 
and  to  the  extent  required  by  the  mechanical  theory. 

Now,  if  a  mixture  of  ice  and  water  becomes  colder 
when  it  is  subjected  to  increased  pressure  without  the 
withdrawal  of  heat,  this  can  only  be  effected  by  some 
free  heat  becoming  latent;  that  is,  some  ice  in  the 
mixture  must  melt  aiad  be  converted  into  water.  In 
this  IS  found  the  reason  why  mechanical  pressure  can 
influence  the  freezing-point.     You  know  that  ice  occu- 


ICE   AND    GLACIEHS.  135 

pies  more  space  than  the  water  from  which  it  is  formed. 
When  water  freezes  in  closed  vessels,  it  can  burst  not 
only  glass  vessels,  but  even  iron  shells.  Inasmuch,  there- 
fore, as  in  the  compressed  mixture  of  ice  and  water  some 
of  the  ice  melts  and  is  converted  into  water,  the  volume 
of  the  mass  diminishes,  and  the  mass  can  yield  more  to 
the  pressure  upon  it  than  it  could  have  done  without 
such  an  alteration  of  the  freezing-point.  Pressure  fur- 
thers in  this  case,  as  is  usual  in  the  interaction  of  various 
natural  forces,  the  occurrence  of  a  change,  that  is  fusion, 
which  is  favourable  to  the  development  of  its  own 
activity. 

In  Sir  W.  Thomson's  experiments,  water  and  ice  were 
confined  in  a  closed  vessel,  from  which  nothing  could 
escape.  The  case  is  somewhat  different  when,  as  with 
glaciers,  the  water  disseminated  in  the  compressed  ice  can 
escape  through  fissures.  The  ice  is  then  compressed, 
but  not  the  water  which  escapes.  The  compressed  ice 
becomes  colder  in  conformity  with  the  lowering  of  its 
freezing-point  by  pressure ;  but  the  freezing-point  of 
water  which  is  not  compressed  is  not  lowered.  Thus 
under  these  circumstances  we  have  ice  colder  than  0°  in 
contact  with  water  at  0°.  The  consequence  is  that 
around  the  compressed  ice  water  continually  freezes  and 
forms  new  ice,  while  on  the  other  hand  part  of  the  com- 
pressed ice  melts. 

This  occurs,  for  instance,  when  only  two  pieces  of  ice 
are  pressed  against  each  other.  By  the  water  which 
freezes  at  their  surfaces  of  contact  they  are  firmly  joined 
into  one  coherent  piece  of  ice.  With  powerful  pressure, 
and  the  chilling  therefore  great,  this  is  quickly  effected ; 
but  even  with  a  feeble  pressure  it  takes  place,  if  suffi- 
cient time  be  given.  Faraday,  who  discovered  this  pro- 
perty, called  it  the  regelation  of  ice-,   the   explanation 


136  ICE   AXD    GLACIERS. 

of  this  phenomenon  has  been  much  controverted ;  I 
have  detailed  to  you  that  which  I  consider  most  satis- 
factory. 

This  freezing  together  of  two  pieces  of  ice  is  very 
readily  effected  by  pieces  of  any  shape,  which  must  not, 
however,  be  at  a  lower  temperature  than  0°,  and  the 
experiment  succeeds  best  when  the  pieces  are  already  in 
the  act  of  melting.^  They  need  only  be  strongly  pressed 
together  for  a  few  minutes  to  make  them  adhere.  The 
more  plane  are  the  surfaces  in  contact,  the  more  com- 
plete is  their  union.  But  a  very  slight  pressure  is  suffi- 
cient if  the  two  pieces  are  left  in  contact  for  some  time.^ 

This  property  of  melting  ice  is  also  utilised  by  boys  in 
making  snow-balls  and  snow-men.  It  is  well  known  that 
this  only  succeeds  either  when  the  snow  is  already  melt- 
ing, or  at  any  rate  is  only  so  much  lower  than  O''  that 
the  warmth  of  the  hand  is  sufficient  to  raise  it  to  this 
temperature.  Very  cold  snow  is  a  dry  loose  powder 
which  does  not  stick  together. 

The  process  which  children  carry  out  on  a  small  scale 
in  making  snow-balls,  takes  place  in  glaciers  on  the  very 
largest  scale.  The  deeper  layers  of  what  was  originally 
fine  loose  neve  are  compressed  by  the  huge  masses  rest- 
ing on  them,  often  amounting  to  several  hundred  feet, 
and  under  this  pressure  they  cohere  with  an  ever  firmer 
and  closer  structure.  The  freshly-fallen  snow  originally 
consisted  of  delicate  microscopically  fine  ice  spicules, 
united  and  forming  delicate  six-rayed,  feathery  stars  of 
extreme  beauty.  As  often  as  the  upper  layers  of  the 
snow-fields  are  exposed  to  the  sun's  rays,  some  of  the 
snow  melts ;  water  permeates  the  mass,  and  on  reaching 

'  In  the  Lectnrf^  a  series  of  small  cylinders  of  ice,  which  had  been  pre- 
pared by  a  method  to  be  afterwards  described,  were  pressed  with  their  plane 
ends  against  each  other,  and  thus  a  cylindrical  bar  of  ice  produced. 

*  Vide  the  additions  at  the  end  of  this  Lecture. 


ICE   AM)   GLACIEKS. 


137 


the  lower  layers  of  still  colder  snow,  it  again  freezes; 
thus  it  is  that  the  firn  first  becomes  granular  and  ac- 
quires the  temperature  of  the  freezing-point.  But  as  the 
weight  of  the  superincumbent  masses  of  snow  continually 
increases  by  the  firmer  adherence  of  its  individual  granules, 
it  ultimately  changes  into  a  dense  and  perfectly  hard 
mass. 

This  transformation  of  snow  into  ice  may  be  artificially 
effected  by  using  a  corresponding  pressure. 

We  have  here  (Fig.  22)  a  cylindrical  cast-iron  vessel, 
A  A  ;  the  base,   B  B,  is  -p^^  .^2 

held  by  three  screws,  and 
can  be  detached,  so  as  to 
remove  the  cylinder  of  ice 
which  is  formed.  After 
tlie  vessel  has  lain  for  a 
while  in  ice-water,  so  as 
to  reduce  it  to  the  tem- 
perature of  0°,  it  is 
packed  full  of  snow,  and 
then  the  cylindrical  plug, 
C  C,  which  fits  the  inner 
aperture,  but  moves  in  it 
with  gentle  friction,  is 
forced  in  with  the  aid  of 
an  hydraulic  press.  The 
press  used  was  such  that 
the  pressure  to  which  the 
snow  was  exposed  could 
be  increased  to  fifty  atmospheres.  Of  course  the  looser 
snow  contracts  to  a  very  small  volume  under  such  a 
powerful  pressure.  The  pressure  is  removed,  the  cylin- 
drical plug  taken  out,  the  hollow  again  filled  up  with 
snow,  and  the  process  repeated  until  the  entire  form  is 
filled  with  the  mass  of  ice,  which  no  longer  gives  way 


138  ICE   AXD    GLACIERS. 

to  pressure.  The  compressed  snow  which  I  now  take  out, 
you  will  see,  has  been  transformed  into  a  hard,  angular, 
and  translucent  cylinder  of  ice  ;  and  how  hard  it  is, 
appears  from  the  crash  which  ensues  when  I  throw  it  to 
the  ground.  Just  as  the  loose  snow  in  the  glaciers  is 
pressed  together  to  solid  ice,  so  also  in  many  places 
ready-formed  irregular  pieces  of  ice  are  joined  and  form 
clear  and  compact  ice.  This  is  most  remarkable  at  the 
base  of  the  glacier  cascades.  These  are  glacier  falls 
where  the  upper  part  of  the  glacier  ends  at  a  steep  rocky 
wall,  and  blocks  of  ice  shoot  down  as  avalanches  over  the 
edge  of  this  wall.  The  heap  of  shattered  blocks  of  ice 
which  accumulate  become  joined  at  the  foot  of  the  rock- 
wall  to  a  compact,  dense  mass,  which  then  continues  its 
way  downwards  as  glacier.  More  frequent  than  such  cas- 
cades, where  the  giacier-stream  is  quite  dissevered,  are 
places  where  the  base  of  the  valley  has  a  steeper  slope, 
as,  for  instance,  the  places  in  the  Mer  de  Glace  (Fig.  14), 
at  g,  of  the  Cascade  of  the  Glacier  du  Geant,  and  at  i  and 
h  of  the  great  terminal  cascade  of  the  Glacier  des  Bois. 
The  ice  splits  there  into  thousands  of  banks  and  cliffs, 
which  then  recombine  towards  the  bottom  of  the  steeper 
slope  and  form  a  coherent  mass. 

This  also  we  may  imitate  in  our  ice-mould.  Instead  of 
the  snow  I  take  irregular  pieces  of  ice,  press  them  to- 
gether ;  add  new  pieces  of  ice,  press  them  again,  and  so 
on,  until  the  mould  is  full.  When  the  mass  is  taken 
out  it  forms  a  compact  coherent  cylinder  of  tolerably  clear 
ice,  which  has  a  perfectly  sharp  edge,  and  is  an  accm'ate 
copy  of  the  mould. 

This  experiment,  which  was  first  made  by  Tyndall,  shows 
that  a  block  of  ice  may  be  pressed  into  any  mould  just 
like  a  piece  of  wax.  It  might,  perhaps,  be  thought  that 
such  a  block  had,  by  the  pressure  in  the  interior,  been 
first  reduced  to  powder  so  fine  that  it  readily  penetrated 


ICE  AND   GLACIERS.  139 

every  crevice  of  the  mould,  and  then  that  this  powdered 
ice,  like  snow,  was  again  combined  by  freezing.  This  sug- 
gests itself  the  more  readily,  since  while  the  press  is  being 
worked  a  continual  creaking  and  cracking  is  heard  in  the 
interior  of  the  mould.  Yet  the  mere  aspect  of  the  cylin- 
ders pressed  from  blocks  of  ice  shows  us  that  it  has  not 
been  formed  in  this  manner ;  for  they  are  generally  clearer 
than  the  ice  which  is  produced  from  snow,  and  the  indi- 
vidual larger  pieces  of  ice  which  have  been  used  to  pro- 
duce them  are  recognised,  though  they  are  somewhat 
changed  and  flattened.  This  is  most  beautiful  when 
clear  pieces  of  ice  are  laid  in  the  form  and  the  rest  of 
the  space  stuffed  full  of  snow.  The  cylinder  is  then  seen 
to  consist  of  alternate  layers  of  clear  and  opaque  ice,  the 
former  arising  from  the  pieces  of  ice,  and  the  latter  from 
the  snow  ;  but  here  also  the  pieces  of  ice  seem  pressed 
into  flat  discs. 

These  observations  teach,  then,  that  ice  need  not  be 
completely  smashed  to  fit  into  the  prescribed  mould,  but 
that  it  may  give  way  without  losing  its  coherence.  This 
can  be  still  more  completely  proved,  and  we  can  acquire  a 
still  better  insight  into  the  cause  of  the  pliability  of  ice, 
if  we  press  the  ice  between  two  plane  wooden  boards, 
instead  of  in  the  mould,  into  which  we  cannot  see. 

I  place  first  an  irregular  cylindrical  piece  of  natural 
ice,  taken  from  the  frozen  surface  of  the  river,  with  its 
two  plane  terminal  surfaces  between  the  plates  of  the 
press.  If  I  begin  to  work,  the  block  is  broken  by 
pressure ;  every  crack  which  forms  extends  through 
the  entire  mass  of  the  block  ;  this  splits  into  a  heap  of 
larger  fragments,  which  again  crack  and  are  broken  the 
more  the  press  is  worked.  If  the  pressure  is  relaxed,  all 
these  fragments  are,  indeed,  reunited  by  freezing,  but 
the  aspect  of  the  whole  indicates  that  the  shape  of  the 
block  has  resulted  less  from  pliability  than  from  fracture, 


140 


ICE   AXD   GLACIERS. 


and  that  the  individual  fragments  have  completely  altered 
their  mutual  positions. 

The  case  is  quite  different  when  one  of  the  cylinders 
which  we  have  formed  from  snow  or  ice  is  placed  between 
the  plates  of  the  press.  As  the  press  is  worked  the  creaking 
and  cracking  is  heard,  but  it  does  not  break  ;  it  gradually 
changes  its  shape,  becomes  lower  and  at  the  same  time 
thicker ;  and  only  when  it  has  been  changed  into  a  tole- 
rably flat  circular  disc  does  it  begin  to  give  way  at  the 
edofes  and  form  cracks,  like  crevasses  on  a  small  scale. 
Fig.  23  shows  the  height  and  diameter  of  such  a  cylinder 
in  its  original  condition  ;  Fig.  24  represents  its  appearance 
after  the  action  of  the  press. 


A  still  stronger  proof  of  the  pliability  of  ice  is  afforded 
when  one  of  our  cylinders  is  forced  through  a  narrow  aper- 
ture. With  this  view  I  place  a  base  on  the  previously 
described  mould,  which  has  a  conical  perforation,  the 
external  aperture  of  which  is  only  two-thirds  the  dia- 
meter of  the  cylindrical  aperture  of  the  form.  Fig.  25 
gives  a  section  of  the  whole.  If  now  I  insert  into  this 
one  of  the  compressed  cylinders  of  ice,  and  force  down  the 
plug  a,  the  ice  is  forced  through  the  narrow  aperture  in 


ICE   AND   GLACIERS. 


141 


Ihe  base.     It  at  first  emerges  as  a  solid  cylinder  of  the 

same  diameter  as  the  aper-  _ 

1      .        ^  ,f  Fig.  25. 

tore  ;  but  as  the  ice  follows 

more  rapidly  in  the  centre 

than  at  the  edges,  the  free 

terminal     surface     of    the 

cylinder    becomes    curved, 

the  end  thickens,  so  that  it 

could  not  be  brought  back 

through  the  aperture,   and 

it  ultimately  splits  off.  Fig. 

26    exhibits     a     series     of 

shapes  which  have  resulted 

in  this  manner.^ 

Here  also  the  cracks  in  the  emerging  cylinder  of  ice 

exhibit  a  surprising  similarity  with  the  longitudinal  rifts 

Fig.  26. 


which  divide  a  glacier  current  where  it  presses  through  a 
narrow  rocky  pass  into  a  wider  valley. 

In  the  cases  which  we  have  described  we  see  the  change 
in  shape  of  the  ice  taking  place  before  our  eyes,  whereby 
the  block  of  ice  retains  its  coherence  without  breaking 
into  individual  pieces.  The  brittle  mass  of  ice  seems 
rather  to  yield  like  a  piece  of  wax. 

A  closer  inspection  of  a  clear  cylinder  of  ice  compressed 

'  Id  this  experiment  the  lower  temperature  of  the  compressed  ice  some- 
times extended  so  far  through  the  iron  form,  that  the  water  in  the  slit 
between  the  base  plate  and  the  cylinder  froze  and  formed  a  thin  sheet  of  ice, 
although  the  pieces  of  ice  as  well  as  the  iron  mould  had  previously  laid  in 
ice-water,  and  could  not  be  colder  than  0°. 


142  ICE   AXD    GLACIERS. 

from  clear  pieces  of  ice,  wliile  the  pressure  is  being  applied, 
shows  us  what  takes  place  in  the  interior  ;  for  we  then  see 
an  innumerable  quantity  of  extremely  fine  radiating  cracks 
shoot  through  it  like  a  turbid  cloud,  which  mostly  dis- 
appear, though  not  completely,  the  moment  the  pressure 
is  suspended.  Such  a  compressed  block  is  distinctly 
more  opaque  immediately  after  the  experiment  than  it 
was  before  ;  and  the  turbidity  arises,  as  may  easily  be 
observed  by  means  of  a  lens,  from  a  great  number 
of  whitish  capillary  lines  crossing  the  interior  of  the 
mass  of  what  is  otherwise  clear.  These  lines  are  the 
optical  expression  of  extremely  fine  cracks  '  which  inter- 
penetrate the  mass  of  the  ice.  Hence  we  may  conclude 
that  the  compressed  block  is  traversed  by  a  great  num- 
ber of  fine  cracks  and  fissures,  which  render  it  pliable ; 
that  its  particles  become  a  little  dispersed,  and  are  there- 
fore withdrawn  from  pressure,  and  that  immediately  after- 
wards the  greater  part  of  the  fissures  disappear,  owing  to 
their  sides  freezing.  Only  in  those  places  in  which  the 
surfaces  of  the  small  displaced  particles  do  not  accurately 
fit  to  each  other  some  fissured  spaces  remain  open,  and  are 
discovered  as  white  lines  and  sm-faces  by  the  reflection  of 
the  light. 

These  cracks  and  laminae  also  become  more  perceptible 
when  the  ice — which,  as  I  before  mentioned,  is  below  zero 
immediately  after  pressure  has  been  applied — is  again 
raised  to  this  temperature  and  begins  to  melt.     The  cre- 

•  These  cracks  are  probably  quite  empty  and  free  from  air,  for  they  are 
also  formed  when  perfectly  clear  and  air-free  pieces  of  ice  are  pressed  in 
the  form  which  has  been  previously  filled  with  water,  and  where,  therefore, 
DO  air  could  gain  access  to  the  pieces  of  ice.  That  such  air-free  crevices 
occur  in  glacier  ice  has  been  already  demonstrated  by  Tyndall.  When  the 
compressed  ice  afterwards  melts,  these  crevices  fill  up  with  water,  no  air 
being  left.  They  are  then,  however,  far  less  visible,  and  the  whole  block 
is  therefore  clearer.  And  just  for  this  reason  they  could  not  originally 
have  been  filled  with  water. 


ICE  AND   GLACIERS.  143 

vices  then  fill  with  water,  and  such  ice  then  consists  of  a 
quantity  of  minute  granules  from  the  size  of  a  pin's  head 
to  that  of  a  pea,  which  are  closely  pushed  into  one  another 
at  the  edges  and  projections,  and  in  part  have  coalesced, 
while  the  narrow  fissures  between  them  are  full  of  water. 
A  block  of  ice  thus  formed  of  ice-granules  adheres  firmly 
together  ;  but  if  particles  be  detached  from  its  corners 
they  are  seen  to  consist  of  these  angular  granules.  Gla- 
cier ice,  when  it  begins  to  melt,  is  seen  to  possess  the 
same  structure,  except  that  the  pieces  of  which  it  consists 
are  mostly  larger  than  in  artificial  ice,  attaining  the  size 
of  a  pigeon's  egg. 

Glacier  ice  and  compressed  ice  are  thus  seen  to  be  sub- 
stances of  a  granular  structure,  in  opposition  to  regularly 
crystallised  ice,  such  as  is  formed  on  the  surface  of  still 
water.  "VVe  here  meet  with  the  same  differences  as  be- 
tween calcareous  spar  and  marble,  both  of  which  consist 
of  carbonate  of  lime ;  but  while  the  former  is  in  large, 
regular  crystals,  the  latter  is  made  up  of  irregularly 
agglomerated  crystalline  grains.  In  calcareous  spar,  as 
well  as  in  crystallised  ice,  the  cracks  produced  by  inserting 
the  point  of  a  knife  extend  through  the  mass,  while  in 
granular  ice  a  crack  which  arises  in  one  of  the  bodies 
where  it  must  yield  does  not  necessarily  spread  beyond 
the  limits  of  the  granule. 

Ice  which  has  been  compressed  from  snow,  and  has 
thus  from  the  outset  consisted  of  innumerable  very  fine 
crystalline  needles,  is  seen  to  be  particularly  plastic. 
Yet  in  appearance  it  materially  differs  from  glacier  ice, 
for  it  is  very  opaque,  owing  to  the  great  quantity  of  air 
which  was  originally  enclosed  in  the  flaky  mass  of  snow, 
and  which  remains  there  as  extremely  minute  bubbles. 
It  can  be  made  clearer  by  pressing  a  cylinder  of  such  ice 
between  wooden  boards  ;  the  air-bubbles  appear  then  on 
the  top  of  the  cylinder  as  a  light  foam.     If  the  discs  are 


144  ICE   AKD   GLACIERS. 

again  broken,  placed  in  the  mould,  and  pressed  into  a 
cylinder,  the  air  may  gradually  be  more  and  more  elimi- 
nated, and  the  ice  be  made  clearer.  No  doubt  in  glaciers 
the  originally  whitish  mass  of  neve  is  thus  gradually 
transformed  into  the  clear,  transparent  ice  of  the  glacier. 

Lastly,  when  streaked  cylinders  of  ice  formed  from 
pieces  of  snow  and  ice  are  pressed  into  discs,  they  become 
finely  streaked,  for  both  their  clear  and  their  opaque  layers 
are  uniformly  extended. 

Ice  thus  striated  occurs  in  numerous  glaciers,  and  is 
no  doubt  caused,  as  Tyndall  maintains,  by  snow  falling 
between  the  blocks  of  ice  ;  this  mixture  of  snow  and  clear 
ice  is  again  compressed  in  the  subsequent  path  of  the 
glacier,  and  gradually  stretched  by  the  motion  of  the 
mass  :  a  process  quite  analogous  to  the  artificial  one  which 
we  hav^e  demonstrated. 

Thus  to  the  eye  of  the  natural  philosopher  the  glacier, 
with  its  wildly-heaped  ice-blocks,  its  desolate,  stony,  and 
muddy  surface,  and  its  threatening  crevasses,  has  become 
a  majestic  stream  whose  peaceful  and  regular  flow  has  no 
parallel ;  which,  according  to  fixed  and  definite  laws,  nar- 
rows, expands,  is  heaped  up,  or,  broken  and  shattered, 
falls  down  precipitous  heights.  If  we  trace  it  beyond  its 
termination  we  see  its  waters,  uniting  to  a  copious  brook, 
burst  through  its  icy  gate  and  flow  away.  Such  a  brook, 
on  emerging  from  the  glacier,  seems  dirty  and  turbid 
enough,  for  it  carries  away  as  powder  the  stone  which 
the  glacier  has  ground.  We  are  disenchanted  at  seeing 
the  wondrously  beautiful  and  transparent  ice  converted 
into  such  muddy  water.  But  the  water  of  the  glacier 
streams  is  as  pure  and  beautiful  as  the  ice,  though  its 
beauty  is  for  the  moment  concealed  and  invisible.  We 
must  search  for  these  waters  after  they  have  passed 
through  a  lake  in  which  they  have  deposited  this  pow- 
dered stone.     The  Lakes  of  Geneva,  of  Thun,  of  Lucerne, 


ICE   AND   GLACIERS.  145 

of  Constance,  the  Lago  Maggiore,  the  Lake  of  Como,  and 
the  Lago  di  Grarda  are  chiefly  fed  with  glacier  waters ; 
their  clearness  and  their  wonderfully  beautiful  blue  or 
blue-green  colour  are  the  delight  of  all  travellers. 

Yet,  leaving  aside  the  beauty  of  these  waters,  and  con- 
sidering only  their  utility,  we  shall  have  still  more  reason 
for  admiration.  The  unsightly  mud,  which  the  glacier 
streams  wash  away,  forms  a  highly  fertile  soil  in  the 
places  where  it  is  deposited ;  for  its  state  of  mechanical 
division  is  extremely  fine,  and  it  is  moreover  an  utterly 
unexhausted  virgin  soil,  rich  in  the  mineral  food  of  plants. 
The  fruitful  layers  of  fine  loam  which  extend  along  the 
whole  Ehine  plain  as  far  as  Belgium,  and  are  known  as 
Loess,  are  nothing  more  than  the  dust  of  ancient  glaciers. 

Then,  again,  the  irrigation  of  a  district,  which  is  effected 
by  the  snow-fields  and  glaciers  of  the  mountains,  is  distin- 
guished from  that  of  other  places  by  its  comparatively 
greater  abundancy,  for  the  moist  air  which  is  driven  over 
the  cold  mountain  peaks  deposits  there  most  of  the  water 
it  contains  in  the  form  of  snow.  In  the  second  place,  the 
snow  melts  most  rapidly  in  summer,  and  thus  the  springs 
which  flow  from  the  snow-fields  are  most  abundant  in  that 
season  of  the  year  in  which  they  are  most  needed. 

Thus  we  ultimately  get  to  know  the  wild,  dead  ice- 
wastes  from  another  point  of  view.  From  them  trickles 
in  thousands  of  rills,  springs,  and  brooks  the  fructifying 
moisture  which  enables  the  industrious  dwellers  of  the 
Alps  to  procure  succulent  vegetation  and  abundance  of 
nourishment  from  the  wild  mountain  slopes.  On  the 
comparatively  small  surface  of  the  Alpine  chain  they 
produce  the  mighty  streams,  the  Ehine,  the  Ehone,  the 
Po,  the  Adige,  the  Inn,  which  for  hundreds  of  miles  form 
broad,  rich  river-valleys,  extending  through  Europe  to  the 
German  Ocean,  the  Mediterranean,  the  Adriatic,  and  the 
Black  Sea.    Let  us  call  to  mind  how  magnificently  Goethe, 


146  ICE  AKD   GLACIERS. 

in  '  Mahomet's  Song,'  has  depicted  the  course  of  the  rocky 
spring,  from  its  origin  beyond  the  clouds  to  its  union 
with  Father  Ocean.  It  would  be  presumptuous  after  him 
to  give  such  a  picture  in  other  than  his  own  words  : — 

And  along,  in  triumph  rolHng, 
Names  he  gives  to  regions  ;   cities 
Grow  amain  beneath  his  feet. 

On  and  ever  on  he  rushes ; 
Spire  and  turret  fiery  crested, 
Marble  palaces,  the  creatures 
Of  his  wealth,  he  leaves  behind. 

Pine-built  houses  bears  the  Atlaa 
On  his  giant  shoulders.     O'er  his 
Head  a  thousand  pennons  rustle, 
Floating  far  upon  the  breezes, 
Tokens  of  hia  majesty. 

And  so  beareth  he  his  brothers, 
And  his  treasures,  and  his  children, 
To  their  primal  sire  expectant, 
All  his  bosom  throbbing,  heaving 
"With  a  wild  tumultuous  joy. 

Theodore  Martin's  Translation, 


ICE  AND    GLACIEKS.  147 


ADDITIONS. 

The  theory  of  the  regelation  of  ice  has  led  to  scientific  discussions 
between  Faraday  and  Tyndall  on  the  one  hand,  and  James  and 
Sir  W.  Thomson  on  the  other.  In  the  text  I  have  adopted  the 
theory  of  the  latter,  and  must  now  accordingly  defend  it. 

Faraday's  experiments  show  that  a  very  slight  pressure,  not 
more  than  that  produced  by  the  capillarity  of  the  layer  of  water 
between  two  pieces  of  ice,  is  sufficient  to  freeze  them  together. 
James  Thomson  observed  that  in  Faraday's  experiments,  pres- 
sure which  could  freeze  them  together  was  not  utterly  wanting. 
I  have  satisfied  myself  by  my  own  experiments  that  only  very 
slight  pressure  is  necessary.  It  must,  however,  be  remembered, 
that  the  smaller  the  pressure  the  longer  will  be  the  time  required 
to  freeze  the  two  pieces,  and  that  then  the  junction  will  be  very 
narrow  and  very  fragile.  Both  these  points  are  readily  explicable 
on  Thomson's  theory.  For  under  a  feeble  pressure  the  diflTerence 
in  temperature  between  ice  and  water  will  be  very  small,  and 
the  latent  heat  will  only  be  slowly  abstracted  from  the  layers  of 
water  in  contact  with  the  pressed  parts  of  the  ice,  so  that  a  long 
time  is  necessary  before  they  freeze.  We  must  further  take  into 
account  that  we  cannot  in  general  consider  that  the  two  surfaces 
are  quite  in  contact ;  under  a  feeble  pressure  which  does  not 
appreciably  alter  their  shape,  they  will  only  touch  in  what  are 
practically  three  points.  A  feeble  total  pressure  on  the  pieces  of 
ice  concentrated  on  such  narrow  surfaces  will  always  produce  a 
tolerably  great  local  pressure  under  the  influence  of  which  some 
ice  will  melt,  and  the  water  thus  formed  will  freeze.  But  the 
bridge  which  joins  them  will  never  be  otherwise  than  narrow. 

Under  stronger  pressure,  which  may  more  completely  alter 
the  shape  of  the  pieces  of  ice,  and  fit  them  against  each  other, 
and  which  will  melt  more  of  the  surfaces  that  are  first  in  con- 
tact, there  will  be  a  greater  difference  between  the  temperature 
of  the  ice  and  water,  and  the  bridges  will  be  more  rapidly 
formed,  and  be  of  greater  extent. 


148  ICE   AND   GLACIERS. 

In  order  to  show  the  slow  action  of  the  small  differences  of 
temperature  which  here  come  into  play,  I  made  the  following 
experiments. 

A  glass  flask  with  a  drawn-out  neck  was  half  filled  with 
water,  which  was  boiled  imril  all  the  air  in  the  flask  was  driven 
out.  The  neck  of  the  flask  was  then  hermetically  sealed.  When 
cooled,  the  flask  was  void  of  air,  and  the  water  within  it  freed 
from  the  pressure  of  the  atmosphere.  As  the  water  thus  pre- 
pared can  be  cooled  considerably  below  0°  C.  before  the  first  ice 
is  formed,  while  when  ice  is  in  the  flask  it  freezes  at  0°  C,  the 
flask  was  in  the  first  instance  placed  in  a  freezing  mixture  until 
the  water  was  changed  into  ice.  It  was  afterwards  permitted  to 
melt  slowly  in  a  place,  the  temperature  of  which  was  +  2°  C, 
until  the  half  of  it  was  liquefied. 

The  flask  thus  half  filled  with  water,  having  a  disc  of  ice 
swimming  upon  it,  was  placed  in  a  mixture  of  ice  and  water, 
being  quite  surrounded  by  the  mixture.  After  an  hour,  the 
disc  within  the  flask  was  frozen  to  the  glass.  By  shaking  the 
flask  the  disc  was  liberated,  but  it  froze  again.  This  occurred 
as  often  as  the  shaking  was  repeated. 

The  flask  was  permitted  to  remain  for  eight  days  in  the 
mixture,  which  was  kept  throughout  at  a  temperature  of  0°  C. 
During  this  time  a  number  of  very  regular  and  sharply  defined 
ice-crystals  were  formed,  and  augmented  very  slowly  in  size. 
This  is  perhaps  the  best  method  of  obtaining  beautifully  formed 
crystals  of  ice. 

While,  therefore,  the  outer  ice  which  had  to  support  the 
pressure  of  the  atmosphere  slowly  melted,  the  water  within  the 
flask,  whose  freezing-point,  on  account  of  a  defect  of  pressure, 
was  0-0075°  C.  higher,  deposited  crystals  of  ice.  The  heat 
abstracted  from  the  water  in  this  operation  had,  moreover,  to 
pass  through  the  glass  of  the  flask,  which,  together  with  the 
small  difference  of  temperature,  explains  the  slowness  of  the 
frerzing  process. 

Now  as  the  pressure  of  one  atmosphere  on  a  square  milli- 
metre amounts  to  about  ten  grammes,  a  piece  of  ice  weighing 
ten  grammes,  which  lies  upon  another  and  touches  it  in  three 
places,  the  total  surface  of  which  is  a  square  millimetre,  will 
produce  on  these  surfaces  a  pressure  of  an  atmosphere.     Ice  will 


ICE   AKD    GLACIEKS.  149 

therefore  be  formed  more  rapidly  in  the  surroundinp;  water  than 
it  was  in  the  flask,  wliere  the  side  of  the  glass  was  interposed 
between  the  ice  and  the  water.  Even  with  a  much  smaller 
weight  the  same  result  will  follow  in  the  course  of  an  hour. 
The  broader  the  bridges  become,  owing  to  the  freshly  formed 
ice,  the  greater  will  be  the  surfaces  over  which  the  pressure 
exerted  by  the  upper  piece  of  ice  is  distributed,  and  the  feebler 
it  will  become ;  so  that  with  such  feeble  pressure  the  bridges 
can  only  slowly  increase,  and  therefore  they  will  be  readily 
broken  when  we  try  to  separate  the  pieces. 

It  cannot,  moreover,  be  doubted,  that  in  Faraday's  experi- 
ments, in  which  two  perforated  discs  of  ice  were  placed  in  con- 
tact on  a  horizontal  glass  rod,  so  that  gravity  exerted  no  pressure, 
capillary  attraction  is  sufficient  to  produce  a  pressure  of  some 
grammes  between  the  plates,  and  the  preceding  discussions  show 
that  such  a  pressure,  if  adequate  time  be  given,  can  form  bridges 
between  the  plates. 

If,  on  the  other  hand,  two  of  the  above-described  cylinders  of 
ice  are  powerfully  pressed  together  by  the  hands,  they  adhere  in 
a  few  minutes  so  firmly,  that  they  can  only  be  detached  by  the 
exertion  of  a  considerable  force,  for  which  indeed  that  of  the 
hands  is  sometimes  inadequate. 

In  my  experiments  I  found  that  the  force  and  rapidity  with 
which  the  pieces  of  ice  united  were  so  entirely  proportional  to 
the  pressure,  that  I  cannot  but  assign  this  as  the  actual  and 
sufficient  cause  of  their  union. 

In  Faraday's  explanation,  according  to  which  regelation  is  due 
to  a  contact  action  of  ice  and  water,  I  find  a  theoretical  difficulty. 
By  the  water  freezing,  a  considerable  quantity  of  latent  heat 
must  be  set  free,  and  it  is  not  clear  what  becomes  of  this. 

Finally,  if  ice  in  its  change  into  water  passes  through  an  inter- 
mediate viscous  condition,  a  mixture  of  ice  and  water  which  was 
kept  for  days  at  a  temperature  of  0°  must  ultimately  assume 
this  condition  in  its  entire  mass,  provided  its  temperature  was 
uniform  throughout ;  this  however  is  never  the  case. 

As  regards  what  is  called  the  plasticity  of  ice,  James  Thomson 
has  given  an  explanation  of  it  in  which  the  formation  of  cracks 
in  the  interior  is  not  presupposed.  No  doubt  when  a  mass  of  ice 
in  diflTerent  parts  of  the  interior  is  exposed  to  diflferent  pressures, 


150  ICE   AND    GLACIERS. 

a  portion  of  the  more  powerfully  compressed  ice  will  melt ;  and 
the  latent  heat  necessary  for  tliis  will  be  supplied  by  the  ice 
which  is  less  strongly  compressed,  and  by  the  water  in  contact 
with  it.  Thus  ice  would  melt  at  the  compressed  places,  and  water 
would  freeze  in  those  which  are  not  pressed  :  ice  would  thus  be 
gradually  transformed  and  yield  to  pressure.  It  is  also  clear 
thitt,  owing  to  the  very  small  conductivity  for  heat  which  ice 
possesses,  a  process  of  this  kind  must  be  extremely  slow,  if  the 
compressed  and  colder  layers  of  ice,  as  in  glaciers,  are  at  con- 
siderable distances  from  the  less  compressed  ones,  and  from  the 
water  which  furnishes  the  heat  for  melting. 

To  test  this  hypothesis,  I  placed  in  a  cylindrical  vessel,  between 
two  discs  of  ice  of  three  inches  in  diameter,  a  smaller  cylindrical 
piece  of  an  inch  in  diameter.  On  the  uppermost  disc  I  placed  a 
wooden  disc,  and  this  I  loaded  with  a  weight  of  twenty  pounds. 
The  section  of  the  narrow  piece  was  thus  exposed  to  a  pressure 
of  more  than  an  atmosphere.  The  whole  vessel  was  packed 
between  pieces  of  ice,  and  left  for  five  days  in  a  room,  the  tem- 
perature of  which  was  a  few  degrees  above  the  freezing-point. 
Under  these  circumstances  the  ice  in  the  vessel,  which  was  ex- 
posed to  the  pressure  of  the  weight,  should  melt,  and  it  might  be 
expected  that  the  narrow  cylinder  on  which  the  pressure  was 
most  powerful  should  have  been  most  melted.  Some  water  was 
indeed  formed  in  the  vessel,  but  mostly  at  the  expense  of  the 
larger  discs  at  the  top  and  bottom,  which  being  nearest  the 
outside  mixture  of  ice  and  water  could  acquire  heat  through  the 
sides  of  the  vessel.  A  small  welt,  too,  of  ice,  was  formed  round 
the  surface  of  contact  of  the  narrower  with  the  lower  broad 
piece,  which  showed  that  the  water,  which  had  been  formed  in 
consequence  of  the  pressure,  had  again  frozen  in  places  in  which 
the  pressure  ceased.  Yet  under  these  circumstances  there  was 
no  appreciable  alteration  in  the  shape  of  the  middle  piece  which 
was  most  compressed. 

This  experiment  shows,  that  although  changes  in  the  shape  of 
the  piecf'S  of  ice  must  take  place  in  the  course  of  time  in  accord- 
ance with  J.  Thomson's  explanation,  by  which  the  more  strongly 
compressed  parts  melt,  and  new  ice  is  formed  at  the  places  which 
are  freed  from  pressure,  these  changes  must  be  extremely  slow 
when  the  thickness  of  the  pieces  of  ice  through  w^hich  the  heat 


ICE   AND    GLACIERS.  151 

is  conducted  is  at  all  considerable.  Any  marked  change  in 
shape  by  melting  in  a  medium  the  temperature  of  which  is 
everywhere  0°,  could  not  occur  without  access  of  external  heat, 
or  from  the  uncompressed  ice  and  water ;  and  with  the  small 
differences  in  temperature  which  here  come  into  play,  and  from 
the  badly  conducting  power  of  ice,  it  must  be  extremely  slow. 

That  on  the  other  hand,  especially  in  granular  ice,  the  forma- 
tion of  cracks,  and  the  displacement  of  the  surfaces  of  those 
cracks,  render  such  a  change  of  form  possible,  is  shown  by  the 
above-described  experiments  on  pressure ;  and  that  in  glacier 
ice  changes  of  form  thus  occur,  follows  from  the  banded  struc- 
ture, and  the  granular  aggregation  which  is  manifest  on  melting, 
and  also  from  the  manner  in  which  the  layers  change  their 
position  when  moved,  and  so  forth.  Hence,  I  doubt  not  that 
Tyndall  has  discovered  the  essential  and  principal  cause  of  the 
motion  of  glaciers,  in  referring  it  to  the  formation  of  cracks  and 
to  regelation. 

I  would  at  the  same  time  observe  that  a  quantity  of  heat, 
which  is  far  from  inconsiderable,  must  be  produced  by 
friction  in  the  larger  glaciers.  It  may  be  easily  shown  by 
calculation,  that  when  a  mass  of  firn  moves  from  the  Col  du 
Geant  to  the  source  of  the  x\rveyron,  the  heat  due  to  the  mecha- 
nical work  would  be  sufficient  to  melt  a  fourteenth  part  of  the 
mass.  And  as  the  friction  must  be  greatest  in  those  places  that 
are  most  compressed,  it  will  at  any  rate  be  sufficient  to  remove 
just  those  parts  of  the  ice  which  offer  most  resistance  to  motion. 

I  will  add  in  conclusion,  that  the  above-described  granular 
structure  of  ice  is  beautifully  shown  in  polarised  light.  If  a 
small  clear  piece  is  pressed  in  the  iron  mould,  so  as  to  form  a 
disc  of  about  five  inches  in  thickness,  this  is  sufficiently  trans- 
parent for  investigation.  Viewed  in  the  polarising  apparatus,  a 
great  number  of  variously  coloured  small  bands  and  rings  are 
seen  in  the  interior ;  and  by  the  arrangement  of  their  colours  it 
is  easy  to  recognise  the  limits  of  the  ice-granules,  which,  heaped 
on  one  another  in  irregular  order  of  their  optical  axes,  constitute 
the  plate.  The  appearance  is  essentially  the  same  when  the 
plate  has  just  been  taken  out  of  the  press,  and  the  cracks  appear 
in  it  as  whitish  lines,  as  afterwards  when  these  crevices  have 
been  filled  up  in  consequence  of  the  ice  beginning  to  melt. 


152  ICE   AKD   GLACIERS. 

In  order  to  explain  the  continued  coherence  of  the  piece  of 
ice  during  its  change  of  form,  it  is  to  be  observed  that  in  general 
the  cracks  in  the  granular  ice  are  only  superficial,  and  do  not 
extend  throughout  its  entire  mass.  This  is  directly  seen  during 
the  pressing  of  the  ice.  The  crevices  form  and  extend  in  dif- 
ferent directions,  like  cracks  produced  by  a  heated  wire  in  a 
glass  tube.  Ice  possesses  a  certain  degree  of  elasticity,  as  may 
be  seen  in  a  thin  flexible  plate.  A  fissured  block  of  ice  of  this 
kind  will  be  able  to  undergo  a  displacement  at  the  two  sides 
which  form  the  crack,  even  when  these  continue  to  adhere  in  the 
unfissured  part  of  the  block.  If  then  part  of  the  fissure  at  first 
formed  is  closed  by  regelation,  the  fissure  can  extend  in  the 
opposite  direction  without  the  continuity  of  the  block  being  at 
any  time  disturbed.  It  seems  to  me  doubtful,  too,  whether  in 
compressed  ice  and  in  glacier  ice,  which  apparently  consists  of 
interlaced  polyhedral  granules,  these  granules,  before  any  at- 
tempt is  made  to  separate  them,  are  completely  detached  from 
each  other,  and  are  not  rather  connected  by  ice  bridges  which 
readily  give  way  ;  and  whether  these  latter  do  not  produce  the 
comparatively  firm  coherence  of  the  apparent  heap  of  granules. 

The  properties  of  ice  here  described  are  interesting  fiom  a 
physical  point  of  view,  for  they  enable  us  to  follow  so  clostly 
the  transition  from  a  crystalline  body  to  a  granular  one  ;  and 
they  give  the  causes  of  the  alteration  of  its  properties  better 
than  in  any  other  well-known  example.  Most  natural  substances 
show  no  regular  crystalline  structure;  our  theoretical  ideas  refer 
almost  exclusively  to  crystallised  and  perfectly  elastic  bodies. 
It  is  precisely  in  this  relationship  that  the  transition  from  fragile 
and  elastic  crystalline  ice  into  plastic  granular  ice  is  so  very 
instructive. 


ON  THE 

INTERACTION  OF  NATURAL  FORCES. 

A  LECTURE  DELIYEEED   FEBRirARY   7,  1854,  AT  KONIGSBEEG, 
IS  PRUSSIA. 


A  NEW  conquest  of  very  general  interest  has  been  recently- 
made  by  natural  philosophy.  In  the  following  pages  I 
will  endeavour  to  give  an  idea  of  the  nature  of  this  con- 
quest. It  has  reference  to  a  new  and  universal  natural 
law,  which  rules  the  actio q  of  natural  forces  in  their 
mutual  relations  towards  each  other,  and  is  as  influential 
on  our  theoretic  views  of  natural  processes  as  it  is  im- 
portant in  their  technical  applications. 

Among  the  practical  arts  which  owe  their  progress  to 
the  development  of  the  natural  sciences,  from  the  con- 
clusion of  the  middle  ages  downwards,  practical  mechanics, 
aided  by  the  mathematical  science  which  bears  the  same 
name,  was  one  of  the  most  prominent.  The  character  of 
the  art  was,  at  the  time  referred  to,  naturally  very  dif- 
ferent from  its  present  one.  Surprised  and  stimulated  by 
its  own  success,  it  thought  no  problem  beyond  its  power, 
and  immediately  attacked  some  of  the  most  difficult  and 
complicated.  Thus  it  was  attempted  to  build  automaton 
figures  which  should  perform  the  functions  of  men  and 


154     ON   THE    INTERACTIOX    OF   NATURAL   FORCES. 

animals.  The  marvel  of  the  last  century  was  Vaucanson's 
duck,  which  fed  and  digested  its  food ;  the  flute-player  of 
tlie  same  artist,  which  moved  all  its  fingers  correctly ;  the 
writing- boy  of  the  elder,  and  the  pianoforte-player  of  the 
younger  Droz  ;  which  latter,  when  performing,  followed  its 
hands  with  its  eyes,  and  at  the  conclusion  of  the  piece 
bowed  courteously  to  the  audience.  That  men  like  those 
mentioned,  whose  talent  might  bear  comparison  with  the 
most  inventive  heads  of  the  present  age,  should  spend  so 
much  time  in  the  construction  of  these  figures  which  we 
at  present  regard  as  the  merest  trifles,  woidd  be  incom- 
prehensible, if  they  had  not  hoped  in  solemn  earnest  to 
solve  a  great  problem.  The  writing-boy  of  the  elder 
Droz  was  publicly  exhibited  in  Germany  some  years  ago. 
Its  wheelwork  is  so  complicated,  that  no  ordinary  head 
would  be  sufficient  to  decipher  its  manner  of  action. 
When,  however,  we  are  informed  that  this  boy  and  its 
constructor,  being  suspected  of  the  black  art,  lay  for  a 
time  in  the  Spanish  Inquisition,  and  with  difficulty  ob- 
tained their  freedom,  we  may  infer  that  in  those  days 
even  such  a  toy  appeared  great  enough  to  excite  doubts 
as  to  its  natural  origin.  And  though  these  artists  may 
not  have  hoped  to  breathe  into  the  creature  of  their  in- 
genuity a  soul  gifted  with  moral  completeness,  still  there 
were  many  who  would  be  willing  to  dispense  with  the 
moral  qualities  of  their  servants,  if  at  the  same  time 
their  immoral  qualities  could  also  be  got  rid  of;  and 
to  accept,  instead  of  the  mutability  of  flesh  and  bones,  ser- 
vices which  should  combine  the  regularity  of  a  machine 
with  the  durability  of  brass  and  steel. 

The  object,  therefore,  which  the  inventive  genius  of  the 
past  century  placed  before  it  with  the  fullest  earnestness, 
and  not  as  a  piece  of  amusement  merely,  was  boldly  chosen, 
and  was  followed  up  with  an  expenditure  of  sagacity  which 
has    contributed  not    a   little    to  enrich  the  mechanical 


ON   THE    INTERACTION    OF   NATURAL   FORCES.     155 

experience  which  a  later  time  knew  how  to  take  advan- 
tage of.  We  no  longer  seek  to  build  machines  which 
shall  fulfil  the  thousand  services  required  of  one  man, 
but  desire,  on  the  contrary,  that  a  machine  shall  perform 
one  service,  and  shall  occupy  in  doing  it  the  place  of  a 
thousand  men. 

From  these  efforts  to  imitate  living  creatures,  another 
idea,  also  by  a  misunderstanding,  seems  to  have  developed 
itself,  and  which,  as  it  were,  formed  the  new  philosopher's 
stone  of  the  seventeenth  and  eighteenth  centuries.  It 
was  now  the  endeavour  to  construct  a  perpetual  motion. 
Under  this  term  was  understood  a  machine,  which, 
without  being  wound  up,  without  consuming  in  the 
working  of  it  falling  water,  wind,  or  any  other  natural 
force,  should  still  continue  in  motion,  the  motive  power 
being  perpetually  supplied  by  the  machine  itself.  Beasts 
and  human  beings  seemed  to  correspond  to  the  idea  of 
such  an  apparatus,  for  they  moved  themselves  ener- 
getically and  incessantly  as  long  as  they  lived,  and 
were  never  wound  up  ;  nobody  set  them  in  motion.  A 
connexion  between  the  supply  of  nourishment  and  the 
development  of  force  did  not  make  itself  apparent.  The 
nourishment  seemed  only  necessary  to  grease,  as  it 
were,  the  wheelwork  of  the  animal  machine,  to  replace 
what  was  used  up,  and  to  renew  the  old.  The  develop- 
ment of  force  out  of  itself  seemed  to  be  the  essential 
peculiarity,  the  real  quintessence  of  organic  life.  If, 
therefore,  men  were  to  be  constructed,  a  perpetual  motion 
must  first  be  found. 

Another  hope  also  seemed  to  take  up  incidentally  the 
second  place,  which  in  our  wiser  age  would  certainly  have 
claimed  the  first  rank  in  the  thoughts  of  men.  The  per- 
petual motion  was  to  produce  work  inexhaustibly  without 
corresponding  consumption,  that  is  to  say,  out  of  nothing. 
Work,  however,  is  money.  Here,  therefore,  the  great 
8 


156     ox  THE   INTERACTION   OF   NATURAL   FORCES. 

practical  problem  which  the  cunning  heads  of  all  cen- 
turies have  followed  in  the  most  diverse  ways,  namely,  to 
fabricate  money  out  of  nothing,  invited  solution.  The 
similarity  with  the  philosopher's  stone  sought  by  the 
ancient  chemists  was  complete.  That  also  was  thought 
to  contain  the  quintessence  of  organic  life,  and  to  be 
capable  of  producing  gold. 

The  spur  which  drove  men  to  inquiry  was  sharp,  and 
the  talent  of  some  of  the  seekers  must  not  be  estimated 
as  small.  The  nature  of  the  problem  was  quite  calcu- 
lated to  entice  poring  brains,  to  lead  them  round  a  circle 
for  years,  deceiving  ever  with  new  expectations  which 
vanished  upon  nearer  approach,  and  finally  reducing  these 
dupes  of  hope  to  open  insanity.  The  phantom  could  not 
be  grasped.  It  would  be  impossible  to  give  a  history  of 
these  efforts,  as  the  clearer  heads,  among  whom  the  elder 
Droz  must  be  ranked,  convinced  themselves  of  the  futility 
of  their  experiments,  and  were  naturally  not  inclined  to 
speak  much  about  them.  Bewildered  intellects,  however, 
proclaimed  often  enough  that  they  had  discovered  the 
grand  secret ;  and  as  the  incorrectness  of  their  proceed- 
ings was  always  speedily  manifest,  the  matter  fell  into  bad 
repute,  and  the  opinion  strengthened  itself  more  and 
more  that  the  problem  was  not  capable  of  solution  ;  one 
difficulty  after  another  was  brought  under  the  dominion 
of  mathematical  mechanics,  and  finally  a  point  was 
reached  where  it  could  be  proved,  that  at  least  by  the  use 
of  pure  mechanical  forces  no  perpetual  motion  could  be 
generated. 

We  have  here  arrived  at  the  idea  of  the  driving  force 
or  power  of  a  machine,  and  shall  have  much  to  do  with  it 
in  future.  I  must  therefore  give  an  explanation  of  it. 
The  idea  of  work  is  evidently  transferred  to  machines  by 
comparing  their  performances  with  those  of  men  and 
animals,  to  replace  which  they  were  applied.     We  still 


ox   THE   INTERACTIOX   OF   XATITIAL   FORCES,     157 

reckon  the  work  of  steam-engines  according  to  horse- 
power. The  value  of  manual  labour  is  determined  partly 
by  the  force  which  is  expended  in  it  (a  strong  labourer  is 
valued  more  highly  than  a  weak  one),  partly,  however, 
by  the  skill  which  is  brought  into  action.  Skilled  work- 
men are  not  to  be  had  in  any  quantity  at  a  moment's 
notice  ;  they  must  have  both  talent  and  instruction,  their 
education  requires  both  time  and  trouble.  A  machine, 
on  the  contrary,  which  executes  work  skilfully,  can  always 
be  multiplied  to  any  extent ;  hence  its  skill  has  not  the 
high  value  of  human  skill  in  domains  where  the  latter 
cannot  be  supplied  by  machines.  Thus  the  idea  of  the 
quantity  of  work  in  the  case  of  machines  has  been  limited 
to  the  consideration  of  the  expenditure  of  force  ;  this  was 
the  more  important,  as  indeed  most  machines  are  con- 
structed for  the  express  purposeof  exceeding,  by  the  mag- 
nitude of  their  effects,  the  powers  of  men  and  animals. 
Hence,  in  a  mechanical  sense,  the  idea  of  work  has  become 
identical  with  that  of  the  expenditure  of  force,  and  in 
this  way  I  will  apply  it  in  the  following  pages. 

How,  then,  can  we  measure  this  expenditui'e,  and  com- 
pare it  in  the  case  of  different  machines  ? 

I  must  here  conduct  you  a  portion  of  the  way — as 
short  a  portion  as  possible — over  the  uninviting  field  of 
mathematico-mechanical  ideas,  in  order  to  bring  you  to 
a  point  of  view  from  which  a  more  rewarding  prospect 
will  open.  And  though  the  example  which  I  will  here 
choose,  namely,  that  of  a  water-mill  with  iron  hammer, 
appears  to  be  tolerably  romantic,  still,  alas  !  I  must  leave 
the  dark  forest  valley,  the  foaming  brook,  the  spark- 
emitting  anvil,  and  the  black  Cyclops  wholly  out  of  sight, 
and  beg  a  moment's  attention  for  the  less  poetic  side  of 
the  question,  namely,  the  machinery.  This  is  driven  by  a 
water-wheel,  which  in  its  turn  is  set  in  motion  by  the 
falling  water.    The  axle  of  the  water-wheel  has  at  certain 


158     ox   THE    IXTERACTION    OF   NATURAL    FORCES. 

places  small  projections,  thumbs,  wliich,  during  the  rota- 
tion, lift  the  heavy  hammer  and  permit  it  to  fall  again. 
The  falling  hammer  belabours  the  mass  of  metal,  which 
is  introduced  beneath  it.  The  work  therefore  done  by 
the  machine  consists,  in  this  case,  in  the  lifting  of  the 
hammer,  to  do  which  the  gravity  of  the  latter  must  be 
overcome.  The  expenditure  of  force  will  in  the  first 
place,  other  circumstances  being  equal,  be  proportional 
to  the  weight  of  the  hammer ;  it  will,  for  example,  be 
double  when  the  weight  of  the  hammer  is  doubled.  But 
the  action  of  the  hammer  depends  not  upon  its  weight 
alone,  but  also  upon  the  height  from  which  it  falls.  If 
it  falls  through  two  feet,  it  will  produce  a  greater  effect 
than  if  it  falls  through  only  one  foot.  It  is,  however, 
clear  that  if  the  machine,  with  a  certain  expenditure  of 
force,  lifts  the  hammer  a  foot  in  height,  the  same  amount 
of  force  must  be  expended  to  raise  it  a  second  foot  in 
height.  The  work  is  therefore  not  only  doubled  when 
the  weight  of  the  hammer  is  increased  twofold,  but  also 
when  the  space  through  which  it  falls  is  doubled.  From 
this  it  is  easy  to  see  that  the  work  must  be  measured  by 
the  product  of  the  weight  into  the  space  through  which 
it  ascends.  And  in  this  way,  indeed,  we  measure  in 
mechanics.  The  unit  of  work  is  a  foot-pound,  that  is,  a 
pound  weight  raised  to  the  height  of  one  foot. 

While  the  work  in  this  case  consists  in  the  raising  of 
the  heavy  hammer-head,  the  driving  force  which  sets  the 
latter  in  motion  is  generated  by  falling  water.  It  is  not 
necessary  that  the  water  should  fall  vertically,  it  can  also 
flow  in  a  moderately  inclined  bed  ;  but  it  must  always, 
where  it  has  water-mills  to  set  in  motion,  move  from  a 
higher  to  a  lower  position.  Experiment  and  theory 
concur  in  teaching,  that  when  a  hammer  of  a  hundred- 
weight is  to  be  raised  one  foot,  to  accomplish  this  at 
least  a  hundredweight  of  water  must  fall  through  the 


ON   THE    INTERACTION   OF   NATURAL   FORCES.     159 

space  of  one  foot ;  or  what  is  equivalent  to  this,  two 
hundredweight  must  fall  half  a  foot,  or  four  hundred- 
weight a  quarter  of  a  foot,  &c.  In  short,  if  we  multiply 
the  weight  of  the  falling  water  by  the  height  through 
which  it  falls,  and  regard,  as  before,  the  product  as  the 
measure  of  the  work,  then  the  work  performed  by  the 
machine  in  raising  the  hammer  can,  in  the  most  favour- 
able case,  be  only  equal  to  the  number  of  foot-pounds  of 
water  which  have  fallen  in  the  same  time.  In  practice, 
indeed,  this  ratio  is  by  no  means  attained :  a  great  portion 
of  the  work  of  the  falling  water  escapes  unused,  inasmuch 
as  part  of  the  force  is  willingly  sacrificed  for  the  sake  of 
obtaining  greater  speed. 

I  will  further  remark,  that  this  relation  remains  un- 
changed whether  the  hammer  is  driven  immediately  by 
the  axle  of  the  wheel,  or  whether — by  the  intervention 
of  wheelwork,  endless  screws,  pulleys,  ropes — the  motion 
is  transferred  to  the  hammer.  We  may,  indeed,  by  such 
arrangements  succeed  in  raising  a  hammer  of  ten  hun- 
dredweight, when  by  the  first  simple  arrangement  the 
elevation  of  a  hammer  of  one  hundredweight  might  alone 
be  possible  ;  but  either  this  heavier  hammer  is  raised  to 
only  one-tenth  of  the  height,  or  tenfold  the  time  is 
required  to  raise  it  to  the  same  height ;  so  that,  however 
we  may  alter,  by  the  interposition  of  machinery,  the 
intensity  of  the  acting  force,  still  in  a  certain  time, 
during  which  the  mill-stream  furnishes  us  with  a  definite 
quantity  of  water,  a  certain  definite  quantity  of  work,  and 
no  more,  can  be  performed. 

Our  machinery,  therefore,  has  in  the  first  place  done 
nothing  more  than  make  use  of  the  gravity  of  the  falling 
water  in  order  to  overpower  the  gravity  of  the  hammer, 
and  to  raise  the  latter.  When  it  has  lifted  the  hammer 
to  the  necessary  height,  it  again  liberates  it,  and  the 
hammer   falls   upon   the  metal   mass   which   is   pushed 


160     ON   THE   INTERACTIOX   OF   NATURAL   FORCES. 

beneath  it.  But  why  does  the  falling  hammer  here  exer- 
cise a  greater  force  than  when  it  is  permitted  simply  to 
press  with  its  own  weight  on  the  mass  of  metal  r  Why  is 
its  power  greater  as  the  height  from  which  it  falls  is 
increased,  and  the  greater  therefore  the  velocity  of  its 
fall  ?  We  find,  in  fact,  that  the  work  performed  by  the 
hammer  is  determined  by  its  velocity.  In  other  cases, 
also,  the  velocity  of  moving  masses  is  a  means  of  pro- 
ducing great  effects.  I  only  remind  you  of  the  destruc- 
tive effects  of  musket-bullets,  which  in  a  state  of  rest  are 
the  most  harmless  things  in  the  world.  I  remind  you  of 
the  windmill,  which  derives  its  force  from  the  moving 
air.  It  may  appear  surprising  that  motion,  which  we  are 
accustomed  to  regard  as  a  non-essential  and  transitory 
endowment  of  bodies,  can  produce  such  great  effects. 
But  the  fact  is,  that  motion  appears  to  us,  under  ordinary 
circumstances,  transitory,  because  the  movement  of  all 
terrestrial  bodies  is  resisted  perpetually  by  other  forces, 
friction,  resistance  of  the  air,  &c.,  so  that  the  motion  is 
incessantly  weakened  and  finally  arrested.  A  body,  how- 
ever, which  is  opposed  by  no  resisting  force,  when  once 
set  in  motion  moves  onward  eternally  with  undiminished 
velocity.  Thus  we  know  that  the  planetary  bodies  have 
moved  without  change  through  space  for  thousands  of 
years.  Only  by  resisting  forces  can  motion  be  diminished 
or  destroyed.  A  moving  body,  such  as  the  hammer  or  the 
musket-ball,  when  it  strikes  against  another,  preFses 
the  latter  together,  or  penetrates  it,  until  the  sum  of  the 
resisting  forces  presented  by  the  body  struck  to  pres- 
sure, or  to  the  separation  of  its  particles,  is  sufficiently 
great  to  destroy  the  motion  of  the  hammer  or  of  the 
bullet.  The  motion  of  a  mass  regarded  as  taking  the 
place  of  working  force  is  called  the  living  force  (vis 
viva)  of  the  mass.  The  word  '  living '  has  of  course  here 
no  reference  whatever  to  living  beings,  but  is  intended  to 


ON   THE   INTERACTION   OF   NATURAL   FOECES.     161 

represent  solely  the  force  of  the  motion  as  distinguished 
from  the  state  of  unchanged  rest — from  the  gravity  of  a 
motionless  body,  for  example,  which  produces  an  incessant 
pressure  against  the  surface  which  supports  it,  but  does 
not  produce  any  motion. 

In  the  case  before  us,  therefore,  we  had  first  power  in 
the  form  of  a  falling  mass  of  water,  then  in  the  form  of 
a  lifted  hammer,  and  thirdly  in  the  form  of  the  living 
force  of  the  falling  hammer.  We  should  transform  the 
third  form  into  the  second,  if  we,  for  example,  permitted 
the  hammer  to  fall  upon  a  highly  elastic  steel  beam 
strong  enough  to  resist  the  shock.  The  hammer  would 
rebound,  and  in  the  most  favourable  case  would  reach  a 
height  equal  to  that  from  which  it  fell,  but  would  never 
rise  higher.  In  this  way  its  mass  would  ascend ;  and  at 
the  moment  when  its  highest  point  has  been  attained  it 
would  represent  the  same  number  of  raised  foot-pounds 
as  before  it  fell,  never  a  greater  number ;  that  is  to  say, 
living  force  can  generate  the  same  amount  of  work  as 
that  expended  in  its  production.  It  is  therefore  equiva- 
lent to  this  quantity  of  work. 

Our  clocks  are  driven  by  means  of  sinking  weights, 
and  our  watches  by  means  of  the  tension  of  springs.  A 
weight  which  lies  on  the  ground,  an  elastic  spring  which 
is  without  tension,  can  produce  no  effects :  to  obtain  such 
we  must  first  raise  the  weight  or  impart  tension  to  the 
spring,  which  is  accomplished  when  we  wind  up  our 
clocks  and  watches.  The  man  who  winds  the  clock  or 
watch  communicates  to  the  weight  or  to  the  spring  a 
certain  amount  of  power,  and  exactly  so  much  as  is  thus 
communicated  is  gradually  given  out  again  during-  the 
following  twenty-four  hours,  the  original  force  being  thus 
slowly  consumed  to  overcome  the  friction  of  the  wheels 
and  the  resistance  which  the  pendulum  encounters  from 
the  air.     The  wheelwork  of  the  clock  therefore  developes 


162     ON   THE   INTERACTION   OF   NATURAL   FORCES. 

no  working  force,  which  was  not  previously  communicated 
to  it,  but  simply  distributes  the  force  given  to  it  uniformly 
over  a  longer  time. 

Into  the  chamber  of  an  air-gun  we  squeeze,  by  means 
of  a  condensing  air-pump,  a  great  quantity  of  air.  \Mien 
we  afterwards  open  the  cock  of  the  gun  and  admit  the 
compressed  air  into  the  barrel,  the  ball  is  driven  out  of 
the  latter  with  a  force  similar  to  that  exerted  by  ignited 
powder.  Now  we  may  determine  the  work  consumed  in 
the  pumping-in  of  the  air,  and  the  living  force  which, 
upon  firing,  is  communicated  to  the  ball,  but  we  shall 
never  find  the  latter  greater  than  the  former.  The  com- 
pressed air  has  generated  no  working  force,  but  simply 
gives  to  the  bullet  tliat  which  has  been  previously  com- 
municated to  it.  And  while  we  have  pumped  for  perhaps 
a  quarter  of  an  hour  to  charge  the  gun,  the  force  is  ex- 
pended in  a  few  seconds  when  the  bullet  is  discharged ; 
but  because  the  action  is  compressed  into  so  short  a  time, 
a  much  greater  velocity  is  imparted  to  the  ball  than 
would  be  possible  to  communicate  to  it  by  the  unaided 
effort  of  the  arm  in  throwing  it. 

From  these  examples  you  observe,  and  the  mathe- 
matical theory  has  corroborated  this  for  all  purely 
mechanical,  that  is  to  say,  for  moving  forces,  that  all  our 
machinery  and  apparatus  generate  no  force,  but  simply 
yield  up  the  power  communicated  to  them  by  natural 
forces, — falling  water,  moving  wind,  or  by  the  muscles  of 
men  and  animals.  After  this  law  had  been  established 
by  the  great  mathematicians  of  the  last  century,  a  per- 
petual motion,  which  should  make  use  solely  of  pure 
mechanical  forces,  such  as  gravity,  elasticity,  pressure  of 
liqidds  and  gases,  coidd  only  be  sought  after  by  be- 
wildered and  ill-instructed  people.  But  there  are  still 
other  natural  forces  which  are  not  reckoned  amonof  the 
purely  moving  forces, — heat,  electricity,  magnetism,  light, 


ON  THE   INTEUACTION"  OF  NATURAL   FORCES,     163 

cliemical  forces,  all  of  which  nevertheless  stand  in  mani- 
fold relation  to  mechanical  processes.  There  is  hardly  a 
natm-al  process  to  be  found  which  is  not  accompanied  by 
mechanical  actions,  or  from  which  mechanical  work  may 
not  be  derived.  Here  the  question  of  a  perpetual  motion 
remained  open  ;  tlie  decision  of  this  question  marks  the 
progress  of  modern  physics,  regarding  which  I  promised 
to  address  you. 

In  the  case  of  the  air-gun,  the  work  to  be  accomplished 
in  the  propulsion  of  the  ball  was  given  by  the  arm  of  the 
man  who  pumped  in  the  air.     In  ordinary  firearms,  the 
condensed  mass  of  air  which  propels  the  bullet  is  obtained 
in  a  totally  different  manner,  namely,  by  the  combustion 
of  the  powder.    Gunpowder  is  transformed  by  combustion 
for  the  most  part  into  gaseous  products,  which  endeavour 
to  occupy  a  much    greater   space   than  that  previously 
taken  up  by  the  volume  of  the  powder^     Thus  you  see 
that,  by  the  use  of  gunpowder,  the  work  which  the  human 
arm  must  accomplish  in  the  case  of  the  air-gun  is  spared. 
In  the  mightiest  of  our  machines,  the  steam-engine,  it 
is  a  strongly  compressed  aeriform  body,  water  vapour, 
which,  by  its  effort  to  expand,  sets  the  machine  in  motion. 
Here  also  we  do  not  condense  the  steam  by  means  of  an 
external  mechanical  force,  but  by  communicating  heat  to 
a  mass  of  water  in  a  closed  boiler,  we  change  this  water 
into  steam,  which,  in  consequence   of  the   limits  of  the 
space,  is  developed  under  strong  pressure.     In  this  case, 
therefore,  it  is  the  heat  communicated  which  generates 
the  mechanical   force.     The  heat  thus  necessary  for  tiie 
machine  we  might  obtain  in  many  ways :  the  ordinary 
method  is  to  procure  it  from  the  combustion  of  coal. 

Combustion  is  a  chemical  process.  A  particular  con- 
stituent of  our  atmosphere,  oxygen,  possesses  a  strong- 
force  of  attraction,  or,  as  is  said  in  chemistry,  a  strong 
affinity  for   the    constituents  of   the   combustible  body, 


164    ON  THE   INTER ACTIOX   OF  NATURAL  FORCES. 

which  affinity,  however,  in  most  cases  can  only  exert 
itself  at  high  temperatures.  As  soon  as  a  portion  of  the 
combustible  body,  for  example  the  coal,  is  sufficiently 
heated,  the  carbon  unites  itself  with  great  violence  to 
the  oxygen  of  the  atmosphere  and  forms  a  peculiar  gas, 
carbonic  acid,  the  same  that  we  see  foaming  from  beer 
and  champagne.  By  this  combination  light  and  heat  are 
generated ;  heat  is  generally  developed  by  any  combina- 
tion of  two  bodies  of  strong  affinity  for  each  other ;  and 
when  the  heat  is  intense  enough,  light  appears.  Hence 
in  the  steam-engine  it  is  chemical  processes  and  chemical 
forces  which  produce  the  astonishing  work  of  these 
machines.  In  like  manner  the  combustion  of  gunpowder 
is  a  chemical  process,  which  in  the  barrel  of  the  gun 
communicates  living  force  to  the  bullet. 

While  now  the  steam-engine  developes  for  us  mechanical 
work  out  of  heat,  we  can  conversely  generate  heat  by  me- 
chanical forces.  Each  impact,  each  act  of  friction  does  it. 
A  skilful  blacksmith  can  render  an  iron  wedge  red-hot  by 
hammering.  The  axles  of  our  carriages  must  be  protected 
by  careful  greasing  from  ignition  through  friction.  Even 
lately  this  property  has  been  applied  on  a  large  scale.  In 
some  factories,  where  a  surplus  of  water  power  is  at  hand, 
this  surplus  is  applied  to  cause  a  strong  iron  plate  to  rotate 
rapidly  upon  another,  so  that  they  become  strongly  heated 
by  the  friction.  The  heat  so  obtained  warms  the  room,  and 
thus  a  stove  without  fuel  is  provided.  Now  could  not 
the  heat  generated  by  the  plates  be  applied  to  a  small 
steam-engine,  wliich  in  its  turn  should  be  able  to  keep 
the  rubbing  plates  in  motion?  The  perpetual  motion 
would  thus  be  at  length  found.  This  question  might  be 
asked,  and  could  not  be  decided  by  the  older  mathematico- 
mechanical  investigations.  I  will  remark  beforehand, 
that  the  general  law  which  I  will  lay  before  you  answers 
the  question  in  the  negative. 


ON   THE   INTERACTION   OF   NATURAL   FORCES.     165 

By  a  similar  plan,  however,  a  speculative  American  set 
some  time  ago  the  industrial  world  of  Europe  in  excite- 
ment. The  magneto-electric  machines  often  made  use  of 
in  the  case  of  rheumatic  disorders  are  well  known  to  the 
public.  By  imparting  a  swift  rotation  to  the  magnet  of 
such  a  machine  we  obtain  powerful  currents  of  electricity. 
If  those  be  conducted  through  water,  the  latter  will  be 
resolved  into  its  two  components,  oxygen  and  hydrogen. 
By  the  combustion  of  hydrogen,  water  is  again  generated. 
If  this  combustion  takes  place,  not  in  atmospheric  air,  of 
which  oxygen  only  constitutes  a  fifth  part,  but  in  pure 
oxygen,  and  if  a  bit  of  chalk  be  placed  in  the  flame,  the 
chalk  will  be  raised  to  its  white  heat,  and  give  us  the 
sun-like  Drummond's  light.  At  the  same  time  the  flame 
developes  a  considerable  quantity  of  heat.  Our  American 
proposed  to  utilise  in  this  way  the  gases  obtained  from 
electrolytic  decomposition,  and  asserted,  that  by  the  com- 
bustion a  sufficient  amount  of  heat  was  generated  to  keep 
a  small  steam-engine  in  action,  which  again  drove  his 
magneto-electric  machine,  decomposed  the  water,  and 
thus  continually  prepared  its  own  fuel.  This  would  cer- 
tainly have  been  the  most  splendid  of  all  discoveries  ;  a 
perpetual  motion  which,  besides  the  force  that  kept  it 
going,  generated  light  like  the  sun,  and  warmed  all  around 
it.  The  matter  was  by  no  means  badly  thought  out.  Each 
practical  step  in  the  affair  was  known  to  be  possible ;  but 
those  who  at  that  time  were  acquainted  with  the  phy- 
sical investigations  which  bear  upon  this  subject,  could 
have  affirmed,  on  first  hearing  the  report,  that  the  matter 
was  to  be  numbered  among  the  numerous  stories  of  the 
fable-rich  America ;  and  indeed  a  fable  it  remained. 

It  is  not  necessary  to  multiply  examples  further.  You 
will  infer  from  those  given  in  what  immediate  connection 
heat,  electricity,  magnetism,  light,  and  chemical  affinity, 
stand  with  mechanical  forces. 


106     ON   THE    IXTERACTIOX    OF   NATURAL    FORCES. 

Starting  from  eacli  of  these  different  manifestations  of 
natm-al  forces,  we  can  set  every  other  in  motion,  for  tlie 
most  part  not  in  one  way  merely,  but  in  many  ways.  It 
is  here  as  with  the  weaver's  web, — 

Where  a  step  stirs  a  thousand  threads, 

The  shuttles  shoot  from  side  to  side, 

The  fibres  flow  unseen, 

And  one  shock  strikes  a  thousand  combinations. 

Now  it  is  clear  that  if  by  any  means  we  could  succeed, 
as  the  above  American  professed  to  have  done,  by  me- 
chanical forces,  in  exciting  chemical,  electrical,  or  other 
natural  processes,  which,  by  any  circuit  whatever,  and 
without  altering  permanently  the  active  masses  in  the 
machine,  could  produce  mechanical  force  in  greater  quan- 
tity than  that  at  first  applied,  a  portion  of  the  work  thus 
gained  might  be  made  use  of  to  keep  the  machine  in 
motion,  while  the  rest  of  the  work  might  be  applied  to 
any  other  purpose  whatever.  The  problem  was  to  find, 
in  the  complicated  net  of  reciprocal  actions,  a  track 
through  chemical,  electrical,  magnetical,  and  thermic 
processes,  back  to  mechanical  actions,  which  might  be 
followed  with  a  final  gain  of  mechanical  work  :  thus  would 
the  perpetual  motion  be  found. 

But,  warned  by  the  futility  of  former  experiments,  the 
public  had  become  wiser.  On  the  whole,  people  did  not 
seek  much  after  combinations  which  promised  to  furnish 
a  perpetual  motion,  but  the  question  was  inverted.  It 
was  no  more  asked.  How  can  I  make  use  of  the  known 
and  unknown  relations  of  natural  forces  so  as  to  construct 
a  perpetual  motion?  but  it  was  asked.  If  a  perpetual 
motion  be  impossible,  what  are  the  relations  which  must 
subsist  between  natural  forces  ?  Everything  was  gained 
by  this  inversion  of  the  question.  The  relations  of  natural 
forces  rendered  necessary  by  the  above  assumption,  might 


ox   THE   IXTEEACTION   OF   NATURAL   FORCES.     1G7 

be  easily  and  completely  stated.  It  was  found  that  all 
known  relations  of  forces  harmonise  with  the  consequences 
of  that  assumption,  and  a  series  of  unknown  i  elations  were 
discovered  at  the  same  time,  the  correctness  of  which  re- 
mained to  be  proved.  If  a  single  one  of  them  could  be 
proved  false,  then  a  perpetual  motion  would  be  possible. 

The  first  who  endeavoured  to  travel  this  way  was  a 
Frenchman  named  Carnot,  in  the  year  1824.  In  spite  of 
a  too  limited  conception  of  his  subject,  and  an  incorrect 
view  as  to  the  nature  of  heat,  which  led  him  to  some  er- 
roneous conclusions,  his  experiment  was  not  quite  unsuc- 
cessful. He  discovered  a  law  which  now  bears  his  name, 
and  to  which  I  will  return  further  on. 

His  labours  remained  for  a  long  time  without  notice, 
and  it  was  not  till  eighteen  years  afterwards,  that  is  in 

1842,  that  different  investigators  in  different  countries, 
and  independent  of  Carnot,  laid  hold  of  the  same  thought. 
The  first  who  saw  truly  the  general  law  here  referred  to, 
and  expressed  it  correctly,  was  a  Grerman  physician,  J.  R, 
Mayer  of  Heilbronn,  in  the  year  1842.     A  little  later,  in 

1843,  a  Dane  named  Colding  presented  a  memoir  to  the 
Academy  of  Copenhagen,  in  which  the  same  law  found 
utterance,  and  some  experiments  were  described  for  its 
further  corroboration.  In  England,  Joule  began  about 
the  same  time  to  make  experiments  having  reference  to 
the  same  subject.  We  often  find,  in  the  case  of  questions 
to  the  solution  of  which  the  development  of  science 
points,  that  several  heads,  quite  independent  of  each 
other,  generate  exactly  the  same  series  of  reflections. 

I  myself,  without  being  acquainted  with  either  Mayer 
or  Colding,  and  having  first  made  the  acquaintance  of 
Joule's  experiments  at  the  end  of  my  investigation,  fol- 
lowed the  same  path.  I  endeavoured  to  ascertain  all  the 
relations  between  the  different  natural  processes,  which 
followed  from  our  regarding  them  from  the  above  point  of 


1G8     ON   THE   IXTERACTION   OF   NATURAL   FORCES. 

view.  My  inquiry  was  made  public  in  1847,  in  a  small 
pamphlet  bearing  the  title,  '  On  the  Conservation  of 
Force.'  ^ 

Since  that  time  the  interest  of  the  scientific  public  for 
this  subject  has  gradually  augmented,  particularly  in 
England,  of  which  I  had  an  opportunity  of  convincing 
myself  during  a  visit  last  summer.  A  great  number  of 
the  essential  consequences  of  the  above  manner  of  view- 
ing the  subject,  the  proof  of  which  was  wanting  when  the 
first  theoretic  notions  were  published,  have  since  been 
confirmed  by  experiment,  particularly  by  those  of  Joule ; 
and  during  the  last  year  the  most  eminent  physicist  of 
France,  Regnault,  has  adopted  the  new  mode  of  regarding 
the  question,  and  by  fresh  investigations  on  the  specific 
heat  of  gases  has  contributed  much  to  its  support.  For 
some  important  consequences  the  experimental  proof  is 
still  wanting,  but  the  number  of  confirmations  is  so  pre- 
dominant, that  I  have  not  deemed  it  premature  to  bring 
the  subject  before  even  a  non-scientific  audience. 

How  the  question  has  been  decided  you  may  already 
infer  from  what  has  been  stated.  In  the  series  of  natural 
processes  there  is  no  circuit  to  be  found,  by  which  me- 
chanical force  can  be  gained  without  a  corresponding 
consumption.  The  perpetual  motion  remains  impossible. 
Our  reflections,  however,  gain  thereby  a  higher  interest. 

We  have  thus  far  regarded  the  development  of  force 
by  natural  processes,  only  in  its  relation  to  its  usefulness 
to  man,  as  mechanical  force.  You  now  see  that  we  have 
arrived  at  a  general  law,  which  holds  good  wholly  inde- 
pendent of  the  application  which  man  makes  of  natural 
forces  ;  we  must  therefore  make  the  expression  of  our  law 
correspond  to  this  more  general  significance.  It  is  in  the 
first  place  clear,  that  the  work  which,  by  any  natural  pro- 

'  There  is  a  translation  of  this  important  Essay  in  the  Scientific  Memoirs, 
New  Series,  p.  114.— J.  T. 


ON   THE   INTERACTION   OF   NATURAL   FORCES.     169 

cess  whatever,  is  performed  under  favourable  conditions 
by  a  machine,  and  which  may  be  measured  in  the  way 
already  indicated,  may  be  used  as  a  measure  of  force  com- 
mon to  all.  P'urther,  the  important  question  arises,  If 
the  quantity  of  force  cannot  be  augmented  except  by 
corresponding  consumption,  can  it  be  diminished  or  lost  ? 
For  the  purposes  of  our  machines  it  certainly  can,  if  we 
neglect  the  opportunity  to  convert  natural  processes  to  use, 
but  as  investigation  has  proved,  not  for  nature  as  a  whole. 

In  the  collision  and  friction  of  bodies  against  each 
other,  the  mechanics  of  former  years  assumed  simply  that 
living  force  was  lost.  But  I  have  already  stated  that  each 
collision  and  each  act  of  friction  generates  heat ;  and, 
moreover.  Joule  has  established  by  experiment  the  im- 
portant law,  that  for  every  foot-pound  of  force  which  is 
lost  a  definite  quantity  of  heat  is  always  generated,  and 
that  when  work  is  performed  by  the  consumption  of  heat, 
for  each  foot-pound  thus  gained  a  definite  quantity  of 
heat  disappears.  The  quantity  of  heat  necessary  to  raise 
the  temperature  of  a  pound  of  water  a  degree  of  the  Cen- 
tigrade thermometer,  corresponds  to  a  mechanical  force 
by  which  a  pound  weight  would  be  raised  to  the  height 
of  1,350  feet:  we  name  this  quantity  the  mechanical 
equivalent  of  heat.  I  may  mention  here  that  these  facts 
conduct  of  necessity  to  the  conclusion,  that  heat  is  not,  as 
was  formerly  imagined,  a  fine  imponderable  substance, 
but  that,  like  light,  it  is  a  peculiar  shivering  motion  of 
the  ultimate  particles  of  bodies.  In  collision  and  friction, 
according  to  this  manner  of  viewing  the  subject,  the  mo- 
tion of  the  mass  of  a  body  which  is  apparently  lost  is  con- 
verted into  a  motion  of  the  ultimate  particles  of  the 
body  ;  and  conversely,  when  mechanical  force  is  generated 
by  heat,  the  motion  of  the  ultimate  particles  is  converted 
into  a  motion  of  the  mass. 

Chemical  combinations  generate  heat,  and  the  quantity 


170     ox   THE   IXTEUACTIOX   OF   NATURAL    FOUCES. 

of  this  heat  is  totally  independent  of  the  time  and  steps 
through  which  the  combination  has  been  effected,  pro- 
vided that  other  actions  are  not  at  the  same  time  brought 
into  play.  If,  however,  mechanical  work  is  at  the  same 
time  accomplished,  as  in  the  case  of  the  steam-engine,  we 
obtain  as  much  less  heat  as  is  equivalent  to  this  work. 
The  quantity  of  work  produced  by  chemical  force  is  in 
general  very  great.  A  pound  of  the  purest  coal  gives, 
when  burnt,  sufficient  heat  to  raise  the  temperature  of 
8,086  pounds  of  water  one  degree  of  the  Centigrade  ther- 
mometer ;  from  this  we  can  calculate  that  the  magnitftde 
of  the  chemical  force  of  attraction  between  the  particles 
of  a  pound  of  coal  and  the  quantity  of  oxygen  that  cor- 
responds to  it,  is  capable  of  lifting  a  weight  of  1 00  pounds 
to  a  height  of  twenty  miles.  Unfortunately,  in  our  steam- 
engines  we  have  hitherto  been  able  to  gain  only  the 
smallest  portion  of  this  work,  the  greater  part  is  lost  in 
the  shape  of  heat.  The  best  expansive  engines  give  back 
as  mechanical  work  only  18  per  cent,  of  the  heat  gene- 
rated by  the  fuel. 

From  a  similar  investigation  of  all  the  other  known 
physical  and  chemical  processes,  we  arrive  at  the  conclu- 
sion that  Nature  as  a  whole  possesses  a  store  of  force 
which  cannot  in  any  way  be  either  increased  or  dimi- 
nished, and  that  therefore  the  quantity  of  force  in  Nature 
is  just  as  eternal  and  unalterable  as  the  quantity  of 
matter.  Expressed  in  this  form,  I  have  named  the  general 
law  '  The  Principle  of  the  Conservation  of  Force.' 

We  cannot  create  mechanical  force,  but  we  may  help 
ourselves  from  the  general  storehouse  of  Nature.  The 
brook  and  the  wind,  which  drive  our  mills,  the  forest  and 
the  coal-bed,  which  supply  our  steam-engines  and  warm 
our  rooms,  are  to  us  the  bearers  of  a  small  portion  of  the 
great  natural  supply  which  we  draw  upon  for  our  pur- 
poses, and  the  actions  of  which  we  can  apply  as  we  think 


ON  THE  INTEKACTION  OF  NATUEAL  FOKCES.  171 

fit.  The  possessor  of  a  mill  claims  the  gravity  of  the 
descending  rivulet,  or  the  living  force  of  the  moving 
wind,  as  his  possession.  These  portions  of  the  store  of 
Nature  are  what  give  his  property  its  chief  value. 

Further,  from  the  fact  that  no  portion  of  force  can  he 
absolutely  lost,  it  does  not  follow  that  a  portion  may  not 
be  inapplicable  to  human  purposes.  In  this  respect  the 
inferences  drawn  by  William  Thomson  from  the  law  of 
Carnot  are  of  importance.  This  law,  which  was  discovered 
by  Carnot  during  his  endeavours  to  ascertain  the  relations 
between  heat  and  mechanical  force,  which,  however,  by 
no  means  belongs  to  the  necessary  consequences  of  the 
conservation  of  force,  and  which  Clausius  was  the  first  to 
modify  in  such  a  manner  that  it  no  longer  contradicted 
the  above  general  law,  expresses  a  certain  relation  between 
the  compressibility,  the  capacity  for  heat,  and  the  expan- 
sion by  heat  of  all  bodies.  It  is  not  yet  completely  proved 
in  all  directions,  but  some  remarkable  deductions  having 
been  drawn  from  it,  and  afterwards  proved  to  be  facts  by 
experiment,  it  has  attained  thereby  the  highest  degree  of 
probability.  Besides  the  mathematical  form  in  which 
the  law  was  first  expressed  by  Carnot,  we  can  give  it  the 
following  more  general  expression  : — '  Only  when  heat 
passes  from  a  warmer  to  a  colder  body,  and  even  then 
only  partially,  can  it  be  converted  into  mechanical  work.' 

The  heat  of  a  body  which  we  cannot  cool  further, 
cannot  be  changed  into  another  form  of  force — into 
electric  or  chemical  force  for  example.  Thus  in  our 
steam-engines  we  convert  a  portion  of  the  heat  of  the 
glowing  coal  into  work,  by  permitting  it  to  pass  to  the 
less  warm  water  of  tlie  boiler.  If,  however,  all  the  bodies 
in  Nature  had  the  same  temperature,  it  would  be  impos- 
sible to  convert  any  portion  of  their  heat  into  mechanical 
work.  According  to  this  we  can  divide  the  total  force 
store  of  the  universe  into  two  parts,  one  of  which  is  heat. 


172     ON   THE   INTEEACTION   OF   NATURAL  FORCES. 

and  must  continue  to  be  such ;  the  other,  to  which  a  por- 
tion of  the  heat  of  the  warmer  bodies,  and  the  total  sup- 
ply of  chemical,  mechanical,  electrical,  and  magnetical 
forces  belong,  is  capable  of  the  most  varied  changes  of 
form,  and  constitutes  the  whole  wealth  of  change  which 
takes  place  in  Nature. 

But  the  heat  of  the  warmer  bodies  strives  perpetually 
to  pass  to  bodies  less  warm  by  radiation  and  conduction, 
and  thus  to  establish  an  equilibrium  of  temperature.  At 
each  motion  of  a  terrestrial  body  a  portion  of  mechanical 
force  passes  by  friction  or  collision  into  heat,  of  which 
only  a  part  can  be  converted  back  again  into  mechanical 
force.  This  is  also  generally  the  case  in  every  electrical 
and  chemical  process.  From  this  it  follows  that  the  first 
portion  of  the  store  of  force,  the  unchangeable  heat,  is 
augmented  by  every  natural  process,  while  the  second 
portion,  mechanical,  electrical,  and  chemical  force,  must 
be  diminished  ;  so  that  if  the  universe  be  delivered  over 
to  the  undisturbed  action  of  its  physical  processes,  all 
force  will  finally  pass  into  the  form  of  heat,  and  all  heat 
come  into  a  state  of  equilibrium.  Then  all  possibility  of 
a  further  change  would  be  at  an  end,  and  the  com23lete 
cessation  of  all  natural  processes  must  set  in.  The  life  of 
men,  animals,  and  plants  could  not  of  course  continue  if 
the  sun  had  lost  his  high  temperature,  and  with  it  his 
light, — if  all  the  components  of  the  earth's  surface  had 
closed  those  combinations  which  their  affinities  demand. 
In  short,  the  universe  from  that  time  forward  would  be 
condemned  to  a  state  of  eternal  rest. 

These  consequences  of  the  law  of  Carnot  are,  of  course, 
only  valid  provided  that  the  law,  when  sufficiently  tested, 
proves  to  be  universally  correct.  In  the  mean  time  there 
is  little  prospect  of  the  law  being  proved  incorrect.  At 
all  events,  we  must  admire  the  sagacity  of  Thomson,  who, 
in  the  letters  of  a  long-known  little  mathematical  for- 


ox   THE    INTERACTION    OF    NATURAL    FORCES.     173 

mula,  which  only  speaks  of  the  heat,  volume,  and  pressure 
of  bodies,  was  able  to  discern  consequences  which  threat- 
ened the  universe,  though  certainly  after  an  infinite  period 
of  time,  with  eternal  death. 

I  have  already  given  you  notice  that  our  path  lay 
through  a  thorny  and  unrefreshing  field  of  mathematico- 
meclianical  developments.  We  have  now  left  this  portion 
of  our  road  behind  us.  The  general  principle  which  I 
have  sought  to  lay  before  you  has  conducted  us  to  a  point 
from  which  our  view  is  a  wide  one  ;  and  aided  by  this 
principle,  we  can  now  at  pleasure  regard  this  or  the  other 
side  of  the  surrounding  world  according  as  our  interest 
in  the  matter  leads  us.  A  glance  into  the  narrow  labora- 
tory of  the  physicist,  with  its  small  appliances  and  com- 
plicated abstractions,  will  not  be  so  attractive  as  a  glance 
at  the  wide  heaven  above  us,  the  clouds,  the  rivers,  the 
woods,  and  the  living  beings  around  us.  While  regarding 
the  laws  which  have  been  deduced  from  the  physical 
processes  of  terrestrial  bodies  as  applicable  also  to  the 
heavenly  bodies,  let  me  remind  you  that  the  same  force 
which,  acting  at  the  earth's  surface,  we  call  gravity 
{Schwere\  acts  as  gravitation  in  the  celestial  spaces,  and 
also  manifests  its  power  in  the  motion  of  the  immeasu- 
rably distant  double  stars,  which  are  governed  by  exactly 
the  same  laws  as  those  subsisting  between  the  earth  and 
moon  ;  that  therefore  the  light  and  heat  of  terrestrial 
bodies  do  not  in  any  way  differ  essentially  from  those  of 
the  sun  or  of  the  most  distant  fixed  star ;  that  the  me- 
teoric stones  which  sometimes  fall  from  external  space 
upon  the  earth  are  composed  of  exactly  the  same  simple 
chemical  substances  as  those  with  which  we  are  acquainted. 
We  need,  therefore,  feel  no  scruple  in  granting  that  general 
laws  to  which  all  terrestrial  natural  processes  are  subject 
are  also  valid  for  other  bodies  than  the  earth.  We  will, 
therefore,  make  use  of  our  law  to  glance  over  the  house- 


174  ox  THE  IXTEHACTIOX  OF  XATUEAL  FORCES. 

hold  of  the  universe  with  respect  to  the  store  of  force, 
capable  of  action,  which  it  possesses. 

A  number  of  singular  peculiarities  in  the  structure  of 
our  planetary  system  indicate  that  it  was  once  a  connected 
mass,  with  a  uniform  motion  of  rotation.  Without  such 
an  assumption  it  is  impossible  to  explain  why  all  the  planets 
move  in  the  same  direction  round  the  sun,  why  they  all 
rotate  in  the  same  direction  round  their  axes,  why  the 
planes  of  their  orbits  and  those  of  their  satellites  and 
rings  all  nearly  coincide,  why  all  their  orbits  differ  but 
little  from  circles,  and  much  besides.  From  these  re- 
maininof  indications  of  a  former  state  astronomers  have 
shaped  an  hypothesis  regarding  the  formation  of  our 
planetary  system,  which,  although  from  the  nature  of  the 
case  it  must  ever  remain  an  hypothesis,  still  in  its  special 
traits  is  so  well  supported  by  analogy,  that  it  certainly 
deserves  our  attention  ;  and  the  more  so,  as  this  notion 
in  our  own  home,  and  within  the  walls  of  this  town,^  first 
found  utterance.  It  was  Kant  who,  feeling  great  interest 
in  the  physical  description  of  the  earth  and  the  planetary 
system,  undertook  the  labour  of  studying  the  works  of 
Newton  ;  and,  as  an  evidence  of  the  dejDth  to  which  he 
had  penetrated  into  the  fundamental  ideas  of  Newton, 
seized  the  notion  that  the  same  attractive  force  of  all 
ponderable  matter  which  now  supports  the  motion  of 
the  planets  must  also  aforetime  have  been  able  to  form 
from  matter  loosely  scattered  in  space  the  planetary 
system.  Afterwards,  and  independent  of  Kant,  Laplace, 
the  great  author  of  the  '  Mecanique  celeste,'  laid  hold  of 
the  same  thought,  and  introduced  it  among  astronomers. 

The  commencement  of  our  planetary  system,  in- 
cluding the  sun,  must,  according  to  this,  be  regarded 
as  an  immense  nebulous  mass  which  filled  the  portion 
of  space  now  occupied  by  our  system  far  beyond  the 
>  Konigsberg. 


ox   THE    INTERACTION   OF   NATURAL   FORCES.     175 

limits  of  Neptune,  our  most  distant  planet.  Even  now 
we  discern  in  distant  regions  of  the  firmament  nebulous 
patches  the  light  of  which,  as  spectrum  analysis  teaches, 
is  the  light  of  ignited  gases  ;  and  in  their  spectra  we  see 
more  especially  those  bright  lines  which  are  produced  by 
ignited  hydrogen  and  by  ignited  nitrogen.  Within  our 
system,  also,  comets,  the  crowds  of  shooting  stars,  and  the 
zodiacal  light  exhibit  distinct  traces  of  matter  dispersed 
like  powder,  which  moves,  however,  according  to  the  law 
of  gravitation,  and  is,  at  all  events,  partially  retarded  by 
the  larger  bodies  and  incorporated  in  them.  The  latter 
undoubtedly  happens  with  the  shooting  stars  and  meteoric 
stones  which  come  within  the  range  of  our  atmosphere. 

If  we  calculate  the  density  of  the  mass  of  our  planetary 
system,  according  to  the  above  assumption,  for  the  time 
when  it  was  a  nebulous  sphere,  which  reached  to  the  path 
of  the  outermost  planet,  we  should  find  that  it  would 
require  several  millions  of  cubic  miles  of  such  matter  to 
weigh  a  single  grain. 

The  general  attractive  force  of  all  matter  must,  how- 
ever, impel  these  masses  to  approach  each  other,  and  to 
condense,  so  that  the  nebulous  sphere  became  incessantly 
smaller,  by  which,  according  to  mechanical  laws,  a  motion 
of  rotation  originally  slow,  and  the  existence  of  which 
must  be  assumed,  would  gradually  become  quicker  and 
quicker.  By  the  centrifugal  force,  which  must  act  most 
energetically  in  the  neighbourhood  of  the  equator  of  the 
nebulous  sphere,  masses  could  from  time  to  time  be  torn 
away,  which  afterwards  would  continue  their  courses 
separate  from  the  main  mass,  forming  themselves  into 
single  planets,  or,  similar  to  the  great  original  sphere, 
into  planets  with,  satellites  and  rings,  until  finally  the 
principal  mass  condensed  itself  into  the  sun.  With 
regard  to  the  origin  of  heat  and  light  this  theory  origi- 
nally gave  no  information. 


176  ox  THE  IXTERACTION  OF  NATURAL  FORCES. 

When  the  nebulous  chaos  first  separated  itself  from 
other  fixed  star  masses  it  must  not  only  have  contained 
all  kinds  of  matter  which  was  to  constitute  the  future 
planetary  system,  but  also,  in  accordance  with  our  new 
law,  the  whole  store  of  force  which  at  a  future  time  ought 
to  unfold  therein  its  wealth  of  actions.  Indeed,  in  this 
respect  an  immense  dower  was  bestowed  in  the  shape  of 
the  general  attraction  of  all  the  particles  for  each  other. 
This  force,  which  on  the  earth  exerts  itself  as  gravity, 
acts  in  the  heavenly  spaces  as  gravitation.  As  terrestrial 
gravity  when  it  draws  a  weight  downwards  performs  work 
and  generates  vis  viva,  so  also  the  heavenly  bodies  do  the 
same  when  they  draw  two  portions  of  matter  from  distant 
regions  of  space  towards  each  other. 

The  chemical  forces  must  have  been  also  present,  ready 
to  act ;  but  as  these  forces  can  only  come  into  operation 
by  the  most  intimate  contact  of  the  different  masses,  con- 
densation must  have  taken  place  before  the  play  of  chemical 
forces  began. 

Whether  a  still  further  supply  of  force  in  the  shape  of 
heat  was  present  at  the  commencement  we  do  not  know. 
At  all  events,  by  aid  of  the  law  of  the  equivalence  of  heat 
and  work,  we  find  in  the  mechanical  forces  existing  at  the 
time  to  which  we  refer  such  a  rich  source  of  heat  and  light, 
that  there  is  no  necessity  whatever  to  take  refuge  in  the 
idea  of  a  store  of  these  forces  originally  existing.  When, 
through  condensation  of  the  masses,  their  particles  came 
into  collision  and  clung  to  each  other,  the  vis  vivaoi  their 
motion  would  be  thereby  annihilated,  and  must  reappear 
as  heat.  Already  in  old  theories  it  has  been  calculated 
that  cosmical  masses  must  generate  heat  by  their  col- 
lision, but  it  was  far  from  anybody's  thought  to  make 
even  a  guess  at  the  amount  of  heat  to  be  generated  in 
this  way.  At  present  we  can  give  definite  numerical 
values  with  certainty. 


ox   THE    INTERACTION   OF   NATURAL   FORCES.     177 

Let  us  make  this  addition  to  our  assumption — that,  at 
the  commencement,  the  density  of  the  nebulous  matter 
was  a  vanishinf^  quantity  as  compared  with  the  present 
density  of  the  sun  and  planets  :  we  can  then  calculate 
how  much  work  has  been  performed  by  the  condensation ; 
we  can  further  calculate  how  much  of  this  work  still  exists 
in  the  form  of  mechanical  force,  as  attraction  of  the 
planets  towards  the  sun,  and  as  vis  viva  of  their  motioiL, 
and  find  by  this  how  much  of  the  force  has  been  converted 
into  heat. 

The  result  of  this  calculation^  is,  that  only  about  the 
454th  part  of  the  original  mechanical  force  remains  as 
such,  and  that  the  remainder,  converted  into  heat,  would 
be  sufficient  to  raise  a  mass  of  water  equal  to  the  sun  and 
planets  taken  together,  not  less  than  twenty-eight  millions 
of  degrees  of  the  Centigrade  scale.  For  the  sake  of  compa- 
rison, I  will  mention  that  the  highest  temperature  which 
we  can  produce  by  the  oxyhydrogen  blowpipe,  which  is 
sufficient  to  fuse  and  vaporise  even  platinum,  and  which 
but  few  bodies  can  endure  without  melting,  is  estimated 
at  about  2,000  degrees.  Of  the  action  of  a  temperature 
of  twenty-eight  millions  of  such  degrees  we  can  form  no 
notion.  If  the  mass  of  our  entire  system  were  pure  coal, 
by  the  combustion  of  the  whole  of  it  only  the  3,500th 
part  of  the  above  quantity  would  be  generated.  This 
is  also  clear,  that  such  a  great  development  of  heat  must 
have  presented  the  greatest  obstacle  to  the  speedy  union 
of  the  masses  ;  that  the  greater  part  of  the  heat  must 
have  been  diffused  by  radiation  into  space,  before  the 
masses  could  form  bodies  possessing  the  present  density 
of  the  sun  and  planets,  and  that  these  bodies  must  once 
have  been  in  a  state  of  fiery  fluidity.  This  notion  is  cor- 
roborated by  the  geological  p?iaBnomena  of  our  planet ; 
and  with  regard  to  the  other  planetary  bodies,  the  flat- 
'  See  note  on  page  193. 


178     ox   THE    IXTERACTIOX   OF   NATURAL   FORCES. 

tened  form  of  the  sphere,  which  is  the  form  of  equili- 
brium of  a  fluid  mass,  is  indicative  of  a  former  state  of 
fluidity.  If  I  thus  permit  an  immense  quantity  of  heat 
to  disappear  without  compensation  from  our  system,  the 
principle  of  the  conservation  of  force  is  not  thereby  in- 
vaded. Certainly  for  our  planet  it  is  lost,  but  not  for  the 
universe.  It  has  proceeded  -outwards,  and  daily  proceeds 
outwards  into  infinite  space  ;  and  we  know  not  whether 
the  medium  which  transmits  the  undulations  of  liglit 
and  heat  possesses  an  end  where  the  rays  must  return,  or 
whether  they  eternally  pursue  their  way  through  infinitude. 

The  store  of  force  at  present  possessed  by  our  system  is 
also  equivalent  to  immense  quantities  of  heat.  If  our 
earth  were  by  a  sudden  shock  brought  to  rest  in  her  orbit 
— ^which  is  not  to  be  feared  in  the  existing  arrangement 
of  our  system — by  such  a  shock  a  quantity  of  heat  would 
be  generated  equal  to  that  produced  by  the  combustion  of 
fourteen  such  earths  of  solid  coal.  Making  the  most  un- 
favourable assumption  as  to  its  capacity  for  heat — that 
is,  placing  it  equal  to  that  of  water — the  mass  of  the  earth 
would  thereby  be  heated  11,200  degrees;  it  would,  there- 
fore, be  quite  fused,  and  for  the  most  part  converted  into 
vapom'.  If,  then,  the  earth,  after  having  been  thus 
brought  to  rest,  should  fall  into  the  sun — which,  of 
course,  would  be  the  case — the  quantity  of  heat  deve- 
loped by  the  shock  would  be  400  times  greater. 

Even  now  from  time  to  time  such  a  process  is  repeated 
on  a  small  scale.  There  can  hardly  be  a  doubt  that 
meteors,  fireballs,  and  meteoric  stones  are  masses  which 
belong  to  the  universe,  and  before  coming  into  the 
domain  of  our  earth,  moved  like  the  planets  round  the 
sun.  Only  when  they  enter  our  atmosphere  do  they 
become  visible  and  fa-U  sometimes  to  the  earth.  In  order 
to  explain  the  emission  of  light  by  these  bodies,  and  the 
fact  that  for  some  time  after  their  descent  they  are  very 


ON   THE   INTERACTION   OF   NATURAL   FORCES.     179 

hot,  the  friction  was  long  ago  thought  of  which  they 
experience  in  passing  through  the  air.  We  can  now 
calculate  that  a  velocity  of  3,000  feet  a  second,  supposing 
the  whole  of  the  friction  to  be  expended  in  lieating  the 
solid  mass,  would  raise  a  piece  of  meteoric  iron  1,000''  C. 
in  temperature,  or,  in  other  words,  to  a  vivid  red  heat. 
Now  the  average  velocity  of  the  meteors  seems  to  be 
thirty  to  tifty  times  the  above  amount.  To  compensate 
this,  however,  the  greater  portion  of  the  heat  is  doubtless 
carried  away  by  the  condensed  mass  of  air  which  the 
meteor  drives  before  it.  It  is  known  that  bright  meteors 
generally  leave  a  luminous  trail  behind  them,  which 
probably  consists  of  severed  portions  of  the  red-hot  sur- 
faces. Meteoric  masses  which  fall  to  the  earth  often 
burst  with  a  violent  explosion,  which  may  be  regarded  as 
a  result  of  the  quick  heating.  The  newly-fallen  pieces 
have  been  for  the  most  part  found  hot,  but  not  red-hot, 
which  is  easily  explainable  by  the  circumstance,  that 
during  the  short  time  occupied  by  the  meteor  in  passing 
through  the  atmosphere,  only  a  thin  superficial  layer  is 
heated  to  redness,  while  but  a  small  quantity  of  heat  has 
been  able  to  penetrate  to  the  interior  of  the  mass.  For 
this  reason  the  red  heat  can  speedily  disappear. 

Thus  has  the  falling  of  the  meteoric  stone,  the  minute 
remnant  of  processes  which  seem  to  have  played  an  im- 
portant part  in  the  formation  of  the  heavenly  bodies, 
conducted  us  to  the  present  time,  where  we  pass  from 
the  darkness  of  hypothetical  views  to  the  brightness  of 
knowledge.  In  what  we  have  said,  however,  all  that  is 
hypothetical  is  the  assumption  of  Kant  and  Laplace, 
that  the  masses  of  our  system  were  once  distributed  as 
nebulse  in  space. 

On  account  of  the  rarity  of  the  case,  we  will  still 
further  remark  in  what  close  coincidence  the  results  of 
science  here  stand  with  the  earlier  legends  of  the  human 


180     ON   THE   INTERACTION   OF  NATURAL   FORCES. 

family,  and  the  forebodings  of  poetic  fancy.  The  cos- 
mogony of  ancient  nations  generally  commences  with 
chaos  and  darkness.     Thus  for  example  Mephistopheles 

says : — 

Part  of  the  Part  am  I,  once  All,  in  primal  night, 
Part  of  the  Darkness  which  brought  forth  the  Light, 
The  haughty  Light,  which  now  disputes  the  space, 
And  claims  of  Mother  Night  her  ancient  place. 

Neither  is  the  Mosaic  tradition  very  divergent,  par- 
ticularly when  we  remember  that  that  which  Moses 
names  heaven,  is  different  from  the  blue  dome  above  us, 
and  is  synonymous  with  space,  and  that  the  unformed 
earth  and  the  waters  of  the  great  deep,  which  were 
afterwards  divided  into  waters  above  the  firmament  and 
waters  below  the  firmament,  resembled  the  chaotic  com- 
ponents of  the  world  : — 

'In  the  beginning  God  created  the  heaven  and  the  earth. 

'  And  the  earth  was  without  form,  and  void ;  and  dark- 
ness was  upon  the  face  of  the  deep.  And  the  spirit  of 
God  moved  upon  the  face  of  the  waters.' 

And  just  as  in  nebulous  sphere,  just  become  luminous, 
and  in  the  new  red-hot  liquid  earth  of  our  modern  cosmo- 
gony light  was  not  yet  divided  into  sun  and  stars,  nor  time 
into  day  and  night,  as  it  was  after  the  earth  had  cooled. 

'  And  God  divided  the  light  from  the  darkness. 

'  And  God  called  the  light  day,  and  the  darkness  He 
called  night.  And  the  evening  and  the  morning  were 
the  first  day.' 

And  now,  first,  after  the  waters  had  been  gathered 
together  into  the  sea,  and  the  earth  had  been  laid  dry, 
could  plants  and  animals  be  formed. 

Our  earth  bears  still  the  unmistakeable  traces  of  its 
old  fiery  fluid  condition.  The  granite  formations  of  her 
mountains  exhibit  a  structure,  which  can  only  be  pro- 


ON   THE   INTERACTION   OF   NATURAL   FORCES.     181 

duced  by  the  crystallisation  of  fused  masses.  Investiga- 
tion still  shows  that  the  temperature  in  mines  and 
borings  increases  as  we  descend ;  and  if  this  increase  is 
uniform,  at  the  depth  of  fifty  miles  a  heat  exists  sufficient 
to  fuse  all  our  minerals.  Even  now  our  volcanoes  pro- 
ject from  time  to  time  mighty  masses  of  fused  rocks  from 
their  interior,  as  a  testimony  of  the  heat  which  exists 
there.  But  the  cooled  crust  of  the  earth  has  already 
become  so  thick,  that,  as  may  be  shown  by  calculations  of 
its  conductive  power,  the  heat  coming  to  the  surface 
from  within,  in  comparison  with  that  reaching  the  earth 
from  the  sun,  is  exceedingly  small,  and  increases  the 
temperature  of  the  surface  only  about  g'^^th  of  a  degree 
Centigrade  ;  so  that  the  remnant  of  the  old  store  of  force 
which  is  enclosed  as  heat  within  the  bowels  of  the  earth 
has  a  sensible  influence  upon  the  processes  at  the  earth's 
surftice  only  through  the  instrumentality  of  volcanic 
phaenomena.  Those  processes  owe  their  power  almost 
wholly  to  the  action  of  other  heavenly  bodies,  particu- 
larly to  the  light  and  heat  of  the  sun,  and  partly  also,  in 
the  case  of  the  tides,  to  the  attraction  of  the  sun  and  moon. 
Most  varied  and  numerous  are  the  changes  which  we 
owe  to  the  light  and  heat  of  the  sun.  The  sun  heats  our 
atiDOsphere  irregularly,  the  warm  rarefied  air  ascends, 
while  fresh  cool  air  flows  from  the  sides  to  supply  its 
place  :  in  this  way  winds  are  generated.  This  action  is 
most  powerful  at  the  equator,  the  warm  air  of  which 
incessantly  flows  in  the  upper  regions  of  the  atmosphere 
towards  the  poles ;  while  just  as  persistently  at  the 
eartu's  surface,  the  trade- wind  carries  new  and  cool  air 
to  the  equator.  Without  the  heat  of  the  sun,  all  winds 
must  of  necessity  cease.  Similar  currents  are  produced 
by  the  same  cause  in  the  waters  of  the  sea.  Their 
power  may  be  inferred  from  the  influence  which  in  some 
cases    they   exert    upon    climate.     By    them    the    warm 


182     ON  THE   INTERACTION   OF  NATURAL   FORCES. 

water  of  the  Antilles  is  carried  to  the  British  Isles,  and 
confers  upon  them  a  mild  uniform  warmth,  and  rich 
moisture ;  while,  through  similar  causes,  the  floating  ice 
of  the  North  Pole  is  carried  to  the  coast  of  Newfoundland 
and  produces  raw  cold.  Further,  by  the  heat  of  the  sun 
a  portion  of  the  water  is  converted  into  vapour,  which 
rises  in  the  atmosphere,  is  condensed  to  clouds,  or  falls 
in  rain  and  snow  upon  the  earth,  collects  in  the  form  of 
springs,  brooks,  and  rivers,  and  finally  reaches  the  sea 
again,  after  having  gnawed  the  rocks,  carried  away  light 
earth,  and  thus  performed  its  part  in  the  geologic 
changes  of  the  earth ;  perhaps  besides  all  this  it  has 
driven  our  water-mill  upon  its  way.  If  the  heat  of  the 
sun  were  withdrawn,  there  would  remain  only  a  single 
motion  of  water,  namely,  the  tides,  which  are  produced 
by  the  attraction  of  the  sun  and  moon. 

How  is  it,  now,  with  the  motions  and  the  work  of 
organic  beings  ?  To  the  builders  of  the  automata  of  the 
last  century,  men  and  animals  appeared  as  clockwork 
which  was  never  wound  up,  and  created  the  force  which 
they  exerted  out  of  nothing.  They  did  not  know  how 
to  establish  a  connexion  between  the  nutriment  con- 
sumed and  the  work  generated.  Since,  however,  we 
have  learned  to  discern  in  the  steam-engine  this  origin 
of  mechanical  force,  we  must  inquire  whether  something 
similar  does  not  hold  good  with  regard  to  men.  Indeed, 
the  continuation  of  life  is  dependent  on  the  consumption 
of  nutritive  materials :  these  are  combustible  substances, 
which,  after  digestion  and  being  passed  into  the  blood, 
actually  undergo  a  slow  combustion,  and  finally  enter 
into  almost  the  same  combinations  with  the  oxygen  of 
the  atmosphere  that  are  produced  in  an  open  fire.  As 
the  quantity  of  heat  generated  by  combustion  is  inde- 
pendent of  the  duration  of  the  combustion  and  the  steps 
iu  which  it  occurs,  we  can  calculate  from  the  mass  of  the 


ON   THE   INTERACTION   OF   NATURAL   FORCES.     183 

consumed  material  how  much  heat,  or  its  equivalent 
work,  is  thereby  generated  in  an  animal  body.  Unfor- 
tunately, the  difficulty  of  the  experiments  is  still  very 
great ;  but  within  those  limits  of  accuracy  which  have 
been  as  yet  attainable,  the  experiments  show  that  the 
heat  generated  in  the  animal  body  corresponds  to  the 
amount  which  would  be  generated  by  the  chemical  pro- 
cesses. The  animal  body  therefore  does  not  differ  from 
the  steam-engine  as  regards  the  manner  in  which  it 
obtains  heat  and  force,  but  does  differ  from  it  in  tlie 
manner  in  which  the  force  gained  is  to  be  made  use  of. 
The  body  is,  besides,  more  limited  than  the  machine  in 
the  choice  of  its  fuel ;  the  latter  could  be  heated  with 
sugar,  with  starch-flour,  and  butter,  just  as  well  as  with 
coal  or  wood ;  the  animal  body  must  dissolve  its  mate- 
rials artificially,  and  distribute  them  through  its  system  ; 
it  must,  further,  perpetually  renew  the  used-up  materials 
of  its  organs,  and  as  it  cannot  itself  create  the  matter 
necessary  for  this,  the  matter  must  come  from  without. 
Liebig  was  the  first  to  point  out  these  various  uses  of 
the  consumed  nutriment.  As  material  for  the  perpetual 
renewal  of  the  body,  it  seems  that  certain  definite  albu- 
minous substances  which  appear  in  plants,  and  form  the 
chief  mass  of  the  animal  body,  can  alone  be  used.  They 
form  only  a  portion  of  the  mass  of  nutriment  taken 
daily  ;  the  remainder,  sugar,  starch,  fat,  are  really  only 
materials  for  warming,  and  are  perhaps  not  to  be  super- 
seded by  coal,  simply  because  the  latter  does  not  permit 
itself  to  be  dissolved. 

If,  then,  the  processes  in  the  animal  body  are  not  in 
this  respect  to  be  distinguished  from  inorganic  processes, 
the  question  arises,  whence  comes  the  nutriment  which 
constitutes  the  source  of  the  body's  force  ?  The  answer 
is,  from  the  vegetable  kingdom  ;  for  only  the  material 
of  plants,  or  the  flesh  of  herbivorous  animals,  can  be 


184     ox  THE   INTERACTION   OF  NATURAL   FORCES. 

made  use  of  for  food.  The  animals  which  live  on  plants 
occupy  a  mean  position  between  carnivorous  animals,  in 
which  we  reckon  man,  and  vegetables,  which  the  former 
could  not  make  use  of  immediately  as  nutriment.  In 
hay  and  grass  the  same  nutritive  substances  are  present 
as  in  meal  and  flour,  but  in  less  quantity.  As,  however, 
the  digestive  organs  of  man  are  not  in  a  condition  to 
extract  the  small  quantity  of  the  useful  from  the  great 
excess  of  the  insoluble,  we  submit,  in  the  first  place, 
these  substances  to  the  powerful  digestion  of  the  ox, 
permit  the  nourishment  to  store  itself  in  the  animal's 
body,  in  order  in  the  end  to  gain  it  for  ourselves  in  a  more 
agreeable  and  useful  form.  In  answer  to  our  question, 
therefore,  we  are  referred  to  the  vegetable  world.  Now 
when  what  plants  take  in  and  what  they  give  out  are 
made  the  subjects  of  investigation,  we  find  that  the 
principal  part  of  the  former  consists  in  the  products  of 
combustion  which  are  generated  by  the  animal.  They 
take  the  consumed  carbon  given  off  in  respiration,  as 
carbonic  acid,  from  the  air,  the  consumed  hydrogen  as 
water,  the  nitrogen  in  its  simplest  and  closest  com- 
bination as  ammonia ;  and  from  these  materials,  with  the 
assistance  of  small  ingredients  which  they  take  from  the 
soil,  they  generate  anew  the  compound  combustible  sub- 
stances, albumen,  sugar,  oil,  on  which  the  animal  subsists. 
Here,  therefore,  is  a  circuit  which  appears  to  be  a  per- 
petual store  of  force.  Plants  prepare  fuel  and  nutri- 
ment, animals  consume  these,  burn  them  slowly  in  their 
lungs,  and  from  the  products  of  combustion  the  plants 
again  derive  their  nutriment.  The  latter  is  an  eternal 
source  of  chemical,  the  former  of  mechanical  forces. 
Would  not  the  combination  of  both  organic  kingdoms 
produce  the  perpetual  motion  ?  We  must  not  conclude 
hastily  :  fm'ther  inquiry  shows,  that  plants  are  capable  of 
producing   combustible  substances  only  when  they  are 


ON   THE   INTERACTION   OF   NATURAL   FORCES.     185 

under  the  influence  of  the  sun.  A  portion  of  the  sun's 
rays  exhibits  a  remarkable  relation  to  chemical  forces, — it 
can  produce  and  destroy  chemical  combinations  ;  and  these 
rays,  which  for  the  most  part  are  blue  or  violet,  are  called 
therefore  chemical  rays.  We  make  use  of  their  action  in 
the  production  of  photographs.  Here  compounds  of  silver 
are  decomposed  at  the  place  where  the  sun's  rays  strike 
them.  The  same  rays  overpower  in  the  green  leaves  of 
plants  the  strong  chemical  affinity  of  the  carbon  of  the 
carbonic  acid  for  oxygen,  give  back  the  latter  free  to  the 
atmosphere,  and  accumulate  the  other,  in  combination 
with  other  bodies,  as  woody  fibre,  starch,  oil,  or  resin. 
These  chemically  active  rays  of  the  sun  disappear  com- 
pletely as  soon  as  they  encounter  the  green  portions  of 
the  plants,  and  hence  it  is  that  in  Daguerreotype  images 
the  green  leaves  of  plants  appear  uniformly  black.  In- 
asmuch as  the  light  coming  from  them  does  not  contain 
the  chemical  rays,  it  is  unable  to  act  upon  the  silver 
compounds.  But  besides  the  blue  and  violet,  the  yellow 
rays  play  an  important  part  in  the  growth  of  plants. 
They  also  are  comparatively  strongly  absorbed  by  the 
leaves. 

Hence  a  certain  portion  of  force  disappears  from  the 
sunlight,  while  combustible  substances  are  generated  and 
accumulated  in  plants ;  and  we  can  assume  it  as  very 
probable,  that  the  former  is  the  cause  of  the  latter.  I 
must  indeed  remark,  that  we  are  in  possession  of  no  ex- 
periments from  which  we  might  determine  whether  the 
vis  viva  of  the  sun's  rays  which  have  disappeared  corre- 
sponds to  the  chemical  forces  accumulated  during  the 
same  time ;  and  as  long  as  these  experiments  are  wanting, 
we  cannot  regard  the  stated  relation  as  a  certainty.  If 
this  view  should  prove  correct,  we  derive  from  it  the 
flattering  result,  that  all  force,  by  means  of  which  our 
bodies  live  and  move,  finds  its  source  in  the  piuest  sun- 


ISO     ox   THE   IXTER ACTION   OF   NATURAL   FORCES. 

light ;  and  hence  we  are  all,  in  point  of  nobility,  not 
behind  the  race  of  the  great  monarch  of  Cliina,  who 
heretofore  alone  called  himself  Son  of  the  Sun.  But  it 
must  also  be  conceded,  that  our  lower  fellow-beings,  the 
frog  and  leech,  share  the  same  gethereal  origin,  as  also  the 
whole  vegetable  world,  and  even  the  fuel  which  comes  to 
us  from  the  ages  past,  as  well  as  the  youngest  offspring 
of  the  forest  with  which  we  heat  our  stoves  and  set  our 
machines  in  motion. 

You  see,  then,  that  the  immense  wealth  of  ever- 
changing  meteorological,  climatic,  geological,  and  organic 
processes  of  our  earth  are  almost  wholly  preserved  in 
action  by  the  light-  and  heat-giving  rays  of  the  sun ;  and 
you  see  in  this  a  remarkable  example,  how  Proteus-like 
the  effects  of  a  single  cause,  under  altered  external  con- 
ditions, may  exhibit  itself  in  nature.  Besides  these,  the 
earth  experiences  an  action  of  another  kind  from  its 
central  luminary,  as  well  as  from  its  satellite  the  moon, 
which  exhibits  itself  in  the  remarkable  phsenomenon  of 
the  ebb  and  flow  of  the  tide. 

Each  of  these  bodies  excites,  by  its  attraction  upon  the 
waters  of  the  sea,  two  gigantic  waves,  which  flow  in  the 
same  direction  round  the  world,  as  the  attracting  bodies 
themselves  apparently  do.  Tlie  two  waves  of  the  moon, 
on  account  of  her  greater  nearness,  are  about  3J  times 
as  large  as  those  excited  by  the  sun.  One  of  these  waves 
has  its  crest  on  the  quarter  of  the  earth's  surface  which  is 
turned  towards  the  moon,  the  other  is  at  the  opposite 
side.  Both  these  quarters  possess  the  flow  of  the  tide, 
while  the  regions  which  lie  between  have  the  ebb.  Al- 
though in  the  open  sea  the  height  of  the  tide  amounts  to 
only  about  three  feet,  and  only  in  certain  narrow  channels, 
where  the  moving  water  is  squeezed  together,  rises  to 
thirty  feet,  the  might  of  the  phaenomenon  is  nevertheless 
manifest   from   the   calculation  of   Bessel,  according  to 


ON  THE   INTERACTION   OF  NATURAL   FORCES.     187 

which  a  quarter  of  the  earth  covered  by  the  sea  possesses, 
during  the  flow  of  the  tide,  about  22,000  cubic  miles  of 
water  more  than  during  the  ebb,  and  that  therefore  such 
a  mass  of  water  must,  in  6 J  hours,  flow  from  one  quarter 
of  the  earth  to  the  other. 

The  phsenomenon  of  the  ebb  and  flow,  as  already  recog- 
nised by  Mayer,  combined  with  the  law  of  the  conserva- 
tion of  force,  stands  in  remarkable  connexion  with  the 
question  of  the  stability  of  our  planetary  system.  The 
mechanical  theory  of  the  planetary  motions  discovered 
by  Newton  teaches,  that  if  a  solid  body  in  absolute  vacuo, 
attracted  by  the  sun,  move  around  him  in  the  same 
manner  as  the  planets,  this  motion  will  endure  unchanged 
through  all  eternity. 

Now  we  have  actually  not  only  one,  but  several  such 
planets,  which  move  around  the  sun,  and  by  their  mutual 
attraction  create  little  changes  and  disturbances  in  each 
other's  paths.  Nevertheless  Laplace,  in  his  great  work, 
the  '  Mecanique  celeste,'  has  proved  that  in  our  planetary 
system  all  these  disturbances  increase  and  diminish  peri- 
odically, and  can  never  exceed  certain  limits,  so  that  by 
this  cause  the  eternal  existence  of  the  planetary  system  ia 
unendangered. 

But  I  have  already  named  two  assumptions  which  must 
be  made :  first,  that  the  celestial  spaces  must  be  abso- 
lutely empty ;  and  secondly,  that  the  sun  and  planets 
must  be  solid  bodies.  The  first  is  at  least  the  case  as 
far  as  astronomical  observations  reach,  for  they  have 
never  been  able  to  detect  any  retardation  of  the  planets, 
such  as  would  occur  if  they  moved  in  a  resisting  medium. 
But  on  a  body  of  less  mass,  the  comet  of  Encke,  changes 
are  observed  of  such  a  nature :  this  comet  describes 
ellipses  round  the  sun  which  are  becoming  gradually 
smaller.  If  this  kind  of  motion,  which  certainly  corre- 
sponds to  that  through  a  resisting  medium,  be  actually 


188     0^1  THE   IXTEUACTION   OF  NATtmAL   FOHCES. 

due  to  the  existence  of  such  a  medium 5  a  time  will  come 
when  the  comet  will  strike  the  sun ;  and  a  similar  end 
threatens  all  the  planets,  although  after  a  time,  the 
length  of  which  baffles  our  imagination  to  conceive  of  it. 
But  even  should  the  existence  of  a  resisting  medium  ^ 
appear  doubtful  to  us,  there  is  no  doubt  that  the  planets 
are  not  wholly  composed  of  solid  materials  which  are 
inseparably  bound  together.  Signs  of  the  existence  of  an 
atmosphere  are  observed  on  the  Sun,  on  Venus,  Mars, 
Jupiter,  and  Saturn.  Signs  of  water  and  ice  upon  Mars ; 
and  our  earth  has  undoubtedly  a  fluid  portion  on  its 
sm'face,  and  perhaps  a  still  greater  portion  of  fluid  within 
it.  The  motions  of  the  tides,  however,  produce  friction, 
all  friction  destroys  vis  viva,  and  the  loss  in  this  case  can 
only  affect  the  vis  viva  of  the  planetary  system.  We 
come  thereby  to  the  unavoidable  conclusion,  that  every 
tide,  although  with  infinite  slowness,  still  with  certainty 
diminishes  the  store  of  mechanical  force  of  the  system ; 
and  as  a  consequence  of  this,  the  rotation  of  the  planets 
in  question  round  their  axes  must  become  more  slow. 
The  recent  careful  investigations  of  the  moon's  motion 
made  by  Hansen,  Adams,  and  Delaunay,  have  proved  that 
the  earth  does  experience  such  a  retardation.  According 
to  the  former,  the  length  of  each  sidereal  day  has  in- 
creased since  the  time  of  Hipparchus  by  the  gi^  part  of  a 
second,  and  the  duration  of  a  century  by  half  a  quarter 
of  an  hour  ;  according  to  Adams  and  Sir  W.  Thomson, 
the  increase  has  been  almost  twice  as  great.  A  clock 
which  went  right  at  the  beginning  of  a  century,  would 
be  twenty-two  seconds  in  advance  of  the  earth  at  the  end 
of  the  century.  Laplace  had  denied  the  existence  of 
such  a  retardation  in  the  case  of  the  earth ;  to  ascertain 
the  amount,  the  theory  of  lunar  motion  required  a  greater 
development  than  was  possible  in  his  time.  The  final 
consequence  would  be,  but  after  millions  of  years,  if  in 


ox   THE   IXTERACTIOX   OF   XATUEAL   FORCES.     189 

the  mean  time  tbe  ocean  did  not  become  frozen,  that  one 
side  of  the  earth  would  be  constantly  turned  towards  the 
sun,  and  enjoy  a  perpetual  day,  whereas  the  opposite  side 
would  be  involved  in  eternal  night.  Such  a  position  we 
observe  in  our  moon  with  regard  to  the  earth,  and  also  in 
the  case  of  the  satellites  as  regards  their  planets  ;  it  is, 
perhaps,  due  to  the  action  of  the  mighty  ebb  and  flow  to 
which  these  bodies,  in  the  time  of  their  fiery  fluid  con- 
dition, were  subjected. 

I  would  not  have  brought  forward  these  conclusions, 
which  again  plunge  us  in  the  most  distant  future,  if  they 
were  not  unavoidable.  Physico-mechanical  laws  are,  as 
it  were,  the  telescopes  of  our  spiritual  eye,  which  can 
penetrate  into  the  deepest  night  of  time,  past  and  to 
come. 

Another  essential  question  as  regards  the  future  of  our 
planetary  system  has  reference  to  its  future  temperature 
and  illumination.  As  the  internal  heat  of  the  earth  has 
but  little  influence  on  the  temperature  of  the  surface, 
the  heat  of  the  sun  is  the  only  thing  which  essentially 
affects  the  question.  The  quantity  of  heat  falling  from 
the  sun  during  a  given  time  upon  a  given  portion  of  the 
earth's  surface  may  be  measured,  and  from  this  it  can  be 
calculated  how  much  heat  in  a  given  time  is  sent  out 
from  the  entire  sun.  Such  measurements  have  been 
made  by  the  French  physicist  Pouillet,  and  it  has  been 
found  that  the  sun  gives  out  a  quantity  of  heat  per  hour 
equal  to  that  which  a  layer  of  the  densest  coal  10  feet 
thick  would  give  out  by  its  combustion ;  and  hence  in  a 
year  a  quantity  equal  to  the  combustion  of  a  layer  of 
17  miles.  If  this  heat  were  drawn  uniformly  from  the 
entire  mass  of  the  sun,  its  temperature  would  only  be 
diminished  thereby  1^  of  a  degree  Centigrade  per  year, 
assuming  its  capacity  for  heat  to  be  equal  to  that  of  water. 
These  results  can  give  us  an  idea  of  the  magnitude  of  the 


190     ox   THE   INTERACTION   OF   NATUEAL   FORCES. 

emission,  in  relation  to  the  surface  and  mass  of  the  sun  ; 
but  they  cannot  inform  us  whether  the  sun  radiates 
heat  as  a  glowing  body,  which  since  its  formation  has  its 
heat  accumulated  within  it,  or  whether  a  new  generation 
of  heat  by  chemical  processes  is  continually  taking  place 
at  the  sun's  surface.  At  all  events,  the  law  of  the  con- 
servation of  force  teaches  us  that  no  process  analogous  to 
those  known  at  the  surface  of  the  earth  can  supply  for 
eternity  an  inexhaustible  amount  of  light  and  heat  to 
the  sun.  But  the  same  law  also  teaches  that  the  store  of 
force  at  present  existing,  as  heat,  or  as  what  may  become 
heat,  is  sufficient  for  an  immeasurable  time.  With  re- 
gard to  the  store  of  chemical  force  in  the  sun,  we  can 
form  no  conjecture,  and  the  store  of  heat  there  existing 
can  only  be  determined  by  very  uncertain  estimations. 
If,  however,  we  adopt  the  very  probable  view,  that  the 
remarkably  small  density  of  so  large  a  body  is  caused  by 
its  high  temperature,  and  may  become  greater  in  time,  it 
may  be  calculated  that  if  the  diameter  of  the  sun  were 
diminished  only  the  ten-thousandth  part  of  its  present 
length,  by  this  act  a  sufficient  quantity  of  heat  would  be 
generated  to  cover  the  total  emission  for  2,100  years. 
So  small  a  change  it  would  be  difficult  to  detect  even  by 
the  finest  astronomical  observations. 

Indeed,  from  the  commencement  of  the  period  during 
which  we  possess  historic  accounts,  that  is,  for  a  period  of 
about  4,000  years,  the  temperature  of  the  earth  has  not 
sensibly  diminished.  From  these  old  ages  we  have  cer- 
tainly no  thermometric  observations,  but  we  have  infor- 
mation regarding  the  distribution  of  certain  cultivated 
plants,  the  vine,  the  olive  tree,  which  are  very  sensitive 
to  changes  of  the  mean  annual  temperature,  and  we  find 
that  these  plants  at  the  present  moment  have  the  same 
limits  of  distribution  that  they  had  in  the  times  of 
Abraham  and  Homer;  from  which  we  may  infer  back- 
wards the  constancy  of  the  climate. 


ON   THE   INTERACTION   OF   NATURAL   FORCES.     191 

In  opposition  to  this  it  has  been  urged,  that  here  in 
Prussia  the  German  knights  in  former  times  cultivated 
the  vine,  cellared  their  own  wine  and  drank  it,  which  is 
no  longer  possible.  From  this  the  conclusion  has  been 
drawn,  that  the  heat  of  our  climate  has  diminished  since 
the  time  referred  to.  Against  this,  however.  Dove  has 
cited  the  reports  of  ancient  chroniclers,  according  to 
which,  in  some  peculiarly  hot  years,  the  Prussian  grape 
possessed  somewhat  less  than  its  usual  quantity  of  acid. 
Tlie  fact  also  speaks  not  so  much  for  the  climate  of  the 
country  as  for  the  throats  of  the  Grerman  drinkers. 

But  even  though  the  force  store  of  our  planetary 
system  is  so  immensely  great,  that  by  the  incessant 
emission  which  has  occurred  during  the  period  of  human 
histoiy  it  has  not  been  sensibly  diminished,  even  though 
the  length  of  the  time  which  must  flow  by  before  a  sen- 
sible change  in  the  state  of  our  planetaiy  system  occurs 
is  totally  incapable  of  measurement,  still  the  inexorable 
laws  of  mechanics  indicate  that  this  store  of  force,  which 
can  only  suffer  loss  and  not  gain,  must  be  finally  exhausted. 
Shall  we  terrify  ourselves  by  this  thought  ?  Men  are  in 
the  habit  of  measuring  the  greatness  and  the  wisdom  of 
the  universe  by  the  duration  and  the  profit  which  it  pro- 
mises to  their  own  race ;  but  the  past  history  of  the  earth 
already  shows  what  an  insignificant  moment  th?  duration 
of  the  existence  of  our  race  upon  it  constitutes.  A 
Nineveh  vessel,  a  Koman  sword,  awake  in  us  the  con- 
ception of  grey  antiquity.  What  the  museums  of  Europe 
show  us  of  the  remains  of  Egypt  and  Assyria  we  gaze 
upon  with  silent  astonishment,  and  despair  of  being  able 
to  carry  our  thoughts  back  to  a  period  so  remote.  Still 
must  the  human  race  have  existed  for  ages,  and  multi- 
plied itself  before  the  Pyramids  or  Nineveh  could  have 
been  erected.  We  estimate  the  duration  of  human  his- 
tory at  6,000  years ;  but  immeasurable  as  this  time  may 


192     ON   THE   INTEEACTION   OF   NATURAL   FORCES. 

appear  to  us,  what  is  it  in  comparison  with  the  time 
during  which  the  earth  carried  successive  series  of  rank 
plants  and  mighty  animals,  and  no  men ;  during  which  in 
our  neighbourhood  the  amber- tree  bloomed,  and  dropped 
its  costly  gum  on  the  earth  and  in  the  sea ;  when  in  Sibe- 
ria, Europe,  and  North  America  groves  of  tropical  palms 
flourished  ;  where  gigantic  lizards,  and  after  them  ele- 
phants, whose  mighty  remains  we  still  find  buried  in 
the  earth,  found  a  home?  Different  geologists,  pro- 
ceeding from  different  premises,  have  sought  to  esti- 
mate the  duration  of  the  above-named  creative  period, 
and  vary  from  a  million  to  nine  million  years.  The 
time  during  which  the  earth  generated  organic  beings 
is  again  small  when  compared  with  the  ages  during 
which  the  'world  was  a  ball  of  fused  rocks.  For  the 
duration  of  its  cooling  from  2,000°  to  200°  Centigrade 
the  experiments  of  Bishop  upon  basalt  show  that  about 
350  millions  of  years  would  be  necessary.  And  with  re- 
gard to  the  time  during  which  the  first  nebulous  mass 
condensed  into  our  planetary  system,  our  most  daring 
conjectures  must  cease.  The  history  of  man,  therefore, 
is  but  a  short  ripple  in  the  ocean  of  time.  For  a  much 
longer  series  of  years  than  that  during  which  he  has 
already  occupied  this  world,  the  existence  of  the  present 
state  of  inorganic  nature  favourable  to  the  duration  of 
man  seems  to  be  secured,  so  that  for  ourselves  and  for 
long  generations  after  us  we  have  nothing  to  fear.  But 
tlie  same  forces  of  air  and  water,  and  of  the  volcanic 
interior,  which  produced  former  geological  revolutions, 
and  buried  one  series  of  living  forms  after  another,  act 
still  upon  the  earth's  crust.  They  more  probably  will 
bring  about  the  last  day  of  the  human  race  than  those 
distant  cosmical  alterations  of  which  we  have  spoken, 
forcing  us  perhaps  to  make  way  for  new  and  more  com- 
plete  living   forms,   as   the   lizards   and   the   mammoth 


ON  THE   INTERACTION   OF  NATUHAL   FORCES.    193 

have  given  place  to  us  and   our  fellow-creatures  which 
now  exist. 

Thus  the  thread  which  was  spun  in  darkness  by  those 
who  sought  a  perpetual  motion  has  conducted  us  to  a  uni- 
versal law  of  nature,  which  radiates  light  into  the  distant 
nights  of  the  beginning  and  of  the  end  of  the  history  of 
the  universe.  To  our  own  race  it  permits  a  long  but  not 
an  endless  existence ;  it  threatens  it  with  a  day  of  judg- 
ment, the  dawn  of  which  is  still  happily  obscured.  As 
each  of  us  singly  must  endure  the  thought  of  his  death, 
the  race  must  endure  the  same.  But  above  the  forms  of 
life  gone  by,  the  human  race  has  higher  moral  problems 
before  it,  the  bearer  of  which  it  is,  and  in  the  completion 
of  which  it  fulfils  its  destiny. 


194  ON  THE  INTERACTION'  OF  NATURAL  FORCES. 


NOTE  TO  PAGE   177. 

I  must  here  explain  the  calculation  of  the  heat  which 
must  be  produced  by  the  assumed  condensation  of  the 
bodies  of  our  system  from  scattered  nebulous  matter. 
The  other  calculations,  the  results  of  which  I  have  men- 
tioned, are  to  be  found  partly  in  J.  R.  Mayer's  papers, 
partly  in  Joule's  communications,  and  partly  by  aid  of 
the  known  facts  and  method  of  science :  they  are  easily 
performed. 

The  measure  of  the  work  performed  by  the  condensation 
of  the  mass  from  a  state  of  infinitely  small  density  is  the 
potential  of  the  condensed  mass  upon  itself.  For  a  sphere 
of  uniform  density  of  the  mass  M,  and  the  radius  K,  the 
potential  upon  itself  V — if  we  call  the  mass  of  the  earth 
772,  its  radius  r,  and  the  intensity  of  gravity  at  its 
surface  g — has  the  value 

,,     3    r^M^ 

Let  us  regard  the  bodies  of  our  system  as  such  spheres, 
then  the  total  work  of  condensation  is  equal  to  the  sum 
of  all  their  potentials  on  themselves.  As,  however,  these 
potentials  for  different  spheres  are  to  each  other  as  the 

M^ 

quantity  -— ,  they  all  vanish  in  comparison  with  the  sun  ; 

even  that  of  the  greatest  planet,  Jupiter,  is  only  about  the 
one  himdred-thousandth  part  of  that  of  the  sun ;  in  the 
calculation,  therefore,  it  is  only  necessary  to  introduce  the 
latter. 

To  elevate  the  temperature  of  a  mass  M  of  the  specific 
heat  0-,  t  degrees,  we  need  a  quantity  of  heat  equal  to 


ox   THE    INTEEACTION    OF   NATURAL    FORCES.     195 

Mat ;  this  corresponds,  when  A^  represents  the  mechanical 
equivalent  of  the  unit  of  heat,  to  the  work  kgM.aL  To 
find  the  elevation  of  temperature  produced  by  the  con- 
densation of  the  mass  of  the  sun,  let  us  set 

we  have  then 


5    A.K 


For  a  mass  of  water  equal  to  the  sun  we  have  o-  =  1  ; 
then  the  calculation  with  the  known  values  of  A,  M,  R,  w, 
and  r,  gives 

<  =  28611000°  Cent. 

The  mass  of  the  sun  is  738  times  greater  than  that  of 
all  the  planets  taken  together ;  if,  therefore,  we  desire  to 
make  the  water  mass  equal  to  that  of  the  entire  system, 

we  must  multiply  the  value  of  t  by  the  fraction         .  which 

739 

makes  hardly  a  sensible  alteration  in  the  result. 

When  a  spherical  mass  of  the  radius  R  condenses  more 

and  more  to  the  radius  E^,  the  elevation  of  temperature 

thereby  produced  is 


5*A  .  mcr  1  R,        Rq  J 


or 

3,  rm   r .     R 

5  ARim< 

Supposing,  then,  the  mass  of  the  planetary  system  to  be 
at  the  commencement,  not  a  sphere  of  infinite  radius,  but 
limited,  say  of  the  radius  of  tlje  path  of  Neptune,  which 
is  six  thousand  times  greater  than  the  radius  of  the  sun, 

T> 

the  magnitude  — ^  will  then  be  equal  to  gQoo,  and  the  above 

value  of  t  would  have  to  be  diminished  by  this  inconsi- 
derable amount. 


196     ON  THE   INTERACTION   OF   NATURAL   FORCES. 

From  the  same  formula  we  can  deduce  that  a  dimimition 
of  ^1^  of  the  radius  of  the  sun  would  generate  work  in  a 
water  mass  equal  to  the  sun,  equivalent  to  2,861  degrees 
Centigrade.  And  as,  according  to  Pouillet,  a  quantity  of 
heat  corresponding  to  1 J  degree  is  lost  annually  in  such  a 
mass,  the  condensation  referred  to  would  cover  the  loss  for 
2,289  years. 

If  the  sun,  as  seems  probable,  be  not  everywhere  of  the 
same  density,  but  is  denser  at  the  centre  than  near  the 
surface,  the  potential  of  its  mass  and  the  corresponding 
quantity  of  heat  will  be  still  greater. 

Of  the  now  remaining  mechanical  forces,  the  vu  viva  of 
the  rotation  of  the  heavenly  bodies  round  their  own  axes 
is,  in  comparison  with  the  other  quantities,  very  small, 
and  may  be  neglected.  The  ins  viva  of  the  motion  of 
revolution  round  the  sun,  if  /j,  be  the  mass  of  a  planet, 
and  p  its  distance  from  the  sun,  is 


L  = 


grmfifl 


\R       2p 


h\- 


Omitting  the  quantity  --  as  very  small  compared  with  -— , 
2p  -tv 

and  dividing  by  the  above  value  of  V,  we  obtain 

L     5  ^ 
V^  M* 

The  mass  of  all  the  planets  together  is  ,— —  of  the  mass 

738 

of  the  Sim ;  hence  the  value  of  L  for  the  entire  system  is 


THE  EECENT  PEOGRESS  OF  THE 
THEORY  OF  VISION. 


A    COURSE    OF  LECTURES     DELIVERED    IN    FRANKFORT    AND    HEIDEL- 
BERG, AND   REPUBLISHED   IN    THE   PREUSSISCHE   JAHRBUCHER,  18C8. 

I.   The  Eye  as  an  Optical  Instrument. 

The  physiology  of  the  senses  is  a  border  land  in  which 
the  two  great  divisions  of  human  knowledge,  natural  and 
mental  science,  encroach  on  one  another's  domain;  in 
which  problems  arise  which  are  important  for  both,  and 
which  only  the  combined  labour  of  both  can  solve. 

No  doubfc  the  first  concern  of  physiology  is  only  with 
material  changes  in  material  organs,  and  that  of  the 
special  physiology  of  the  senses  is  with  the  nerves  and 
their  sensations,  so  far  as  these  are  excitations  of  the 
nerves.  But,  in  the  course  of  investigation  into  the 
functions  of  the  organs  of  the  senses,  science  cannot  avoid 
also  considering  the  apprehension  of  external  objects, 
which  is  the  result  of  these  excitations  of  the  nerves, 
and  for  the  simple  reason  that  the  fact  of  a  particular 
state  of  mental  apprehension  often  reveals  to  us  a  nervous 
excitation  which  would  otherwise  have  escaped  our  notice. 
On  the  other  hand,  apprehension  of  external  objects  must 
always  be  an  act  of  our  power  of  realization,  and  must 
therefore  be  accompanied  by  consciousness,  for  it  is  a 
mental  function.  Indeed  the  further  exact  investigation 
of  this  process  has  been  pushed,  the  more  it  has  revealed 
to  us  an  ever-widening  field  of  such  mental  functionsj 


108   KECEXT    PEOGRESS    OF   THE    THEORY   OF   VISION. 

the  results  of  which  are  involved  in  those  acts  of  appre- 
hension by  the  senses  which  at  first  sight  appear  to  be 
most  simple  and  immediate.  These  concealed  functions 
have  been  but  little  discussed,  because  we  are  so  ac- 
customed to  regard  the  apprehension  of  any  external 
object  as  a  complete  and  direct  whole,  which  does  not 
admit  of  analysis. 

It  is  scarcely  necessary  for  me  to  remind  my  present 
readers  of  the  fundamental  importance  of  this  field  of 
inquiry  to  almost  every  other  department  of  science. 
For  apprehension  by  the  senses  supplies  after  all,  directly 
or  indirectly,  the  material  of  all  human  knowledge,  or 
at  least  the  stimulus  necessary  to  develope  every  inborn 
faculty  of  the  mind.  It  supplies  the  basis  for  the  whole 
action  of  man  upon  the  outer  world  ;  and  if  this  stage  of 
mental  processes  is  admitted  to  be  the  simplest  and  lowest 
of  its  kind,  it  is  none  the  less  important  and  interesting. 
For  there  is  little  hope  that  he  who  does  not  begin  at 
the  beginning  of  knowledge  will  ever  arrive  at  its  end. 

It  is  by  this  path  that  the  art  of  experiment,  which 
has  become  so  important  in  natural  science,  found  en- 
trance into  the  hitherto  inaccessible  field  of  mental 
processes.  At  first  this  will  be  only  so  far  as  we  are 
able  by  experiment  to  determine  the  particular  sensible 
impressions  which  call  up  one  or  another  conception 
in  our  consciousness.  But  from  this  first  step  will  follow 
numerous  deductions  as  to  the  natm-e  of  the  mental 
processes  which  contribute  to  the  result.  I  will  therefore 
endeavour  to  give  some  account  of  the  results  of  physi- 
ological inquiries  so  far  as  they  bear  on  the  questions 
above  mentioned. 

I  am  the  more  desirous  of  doing  so  because  I  have 
lately  completed  '  a  complete  survey  of  the  field  of  physio- 
logical optics,  and  am  happy  to  have  an  opportunity  of 

'  Prof.  Helmholtz's  Handbook  of  Physiological  Optics  was  published  at 
Leipzig  in  1867. 


THE  EYE   AS  AN   OPTICAL   INSTRUMExYT.  199 

putting  together  in  a  compendious  form  the  views  and 
deductions  on  the  present  subject  which  might  escape 
notice  among  the  numerous  details  of  a  book  devoted  to 
the  special  objects  of  natural  science.  I  may  state  that 
in  that  work  I  took  great  pains  to  convince  myself  of 
the  truth  of  every  fact  of  the  slightest  importance  by 
personal  observation  and  experiment.  There  is  no  longer 
much  controversy  on  the  more  important  facts  of  obser- 
vation, the  chief  difference  of  opinion  being  as  to  the 
extent  of  certain  individual  differences  of  apprehension 
by  the  senses.  During  the  last  few  years  a  great  number 
of  distinguished  investigators  have,  under  the  influence 
of  the  rapid  progress  of  ophthalmic  medicine,  worked  at 
the  physiology  of  vision ;  and  in  proportion  as  the 
number  of  observed  facts  has  increased,  they  have 
also  become  more  capable  of  scientific  arrangement  and 
explanation.  I  need  not  remind  those  of  my  readers 
who  are  conversant  with  the  subject  how  much  labour 
must  be  expended  to  establish  many  facts  which  appear 
comparatively  simple  and  almost  self-evident. 


To  render  what  follows  understood  in  all  its  bearinofs, 
I  shall  first  describe  the  physical  characters  of  the  eye 
as  an  optical  instrument ;  next  the  physiological  pro- 
cesses of  excitation  and  conduction  in  the  parts  of  the 
nervous  system  which  belong  to  it ;  and  lastly  I  shall 
take  up  the  psychological  question,  how  mental  appre- 
hensions are  produced  by  the  changes  which  take  place  in 
the  optic  nerve. 

The  first  part  of  our  inquiry,  which  cannot  be  passed 
over  because  it  is  the  foundation  of  what  follows,  will 
be  in  great  part  a  repetition  of  what  is  already  generally 
known,  in  order  to  bring  in  what  is  new  in  its  proper 
place.  But  it  is  just  this  part  of  the  subject  whicli 
excites    so  much  interest,  as  the  real  starting  point  of 


200   RECENT   PROGRESS   OF   THE   THEORY   OF   VISION. 

that  remarkable  progress  which  ophthalmic  medicine  has 
made  during  the  last  twenty  years — a  progress  which 
for  its  rapidity  and  scientific  character  is  perhaps  without 
parallel  in  the  history  of  the  healing  art. 

Every  lover  of  his  kind  must  rejoice  in  these  achieve- 
ments which  ward  off  or  remove  so  much  misery  that 
formerly  we  were  powerless  to  help,  but  a  man  of  science 
has  peculiar  reason  to  look  on  them  with  pride.  For 
this  wonderful  advance  has  not  been  achieved  by  groping 
and  lucky  finding,  but  by  deduction  rigidly  followed  out, 
and  tlius  carries  with  it  the  pledge  of  still  future  suc- 
cesses. As  once  astronomy  was  the  pattern  from  which 
the  other  sciences  learned  how  the  right  method  will 
lead  to  success,  so  does  ophthalmic  medicine  now  dis- 
play how  much  may  be  accomplished  in  the  treatment 
of  disease  by  extended  application  of  well-understood 
methods  of  investigation  and  accurate  insight  into  the 
causal  connection  of  phenomena.  It  is  no  wonder  that 
the  right  sort  of  men  were  drawn  to  an  arena  which 
offered  a  prospect  of  new  and  noble  victories  over  the 
opposing  powers  of  nature  to  the  true  scientific  spirit — 
tlie  spirit  of  patient  and  cheerful  work.  It  was  because 
there  were  so  many  of  them  that  the  success  was  so 
brilliant.  Let  me  be  permitted  to  name  out  of  the 
whole  number  a  representative  of  each  of  the  three 
nations  of  common  origin  which  have  contributed  most 
to  the  result :  Von  Grraefe  in  Grermany,  Donders  in 
Holland,  and  Bowman  in  England. 

There  is  -another  point  of  view  from  which  this  advance 
in  ophthalmology  may  be  regarded,  and  that  with  equal 
satisfaction.     Schiller  says  of  science  : — 

AVer  uni  die  Gottin  freit,  suche  in  ihr  nicht  das  Weib.^ 
}Vho  ivoos  the  goddess  must  not  hope  the  wife. 


•  From  Schiller's  Spruche.     Literally,  '  Let  not  him  who  seeks  the  love 
of  a  goddess  expect  to  find  in  her  the  woman.' 


THE    EYE    AS   AN    OPTICAL    INSTRUMENT.  201 

And  history  teaches  us,  what  we  shall  have  opportunity 
of  seeing  in  the  present  inquiry,  that  the  most  important 
practical  results  have  sprung  unexpectedly  out  of  investi- 
gations which  might  seem  to  the  ignorant  mere  busy 
trifling,  and  which  even  those  better  able  to  judge  could 
only  regard  with  the  intellectual  interest  which  pure 
theoretical  inquiry  excites. 


Of  all  our  members  the  eye  has  always  been  held  the 
choicest  gift  of  Nature — the  most  marvellous  product  of 
her  plastic  force.  Poets  and  orators  have  celebrated  its 
praises;  philosophers  have  extolled  it  as  a  crowning 
instance  of  perfection  in  an  organism  ;  and  opticians  have 
tried  to  imitate  it  as  an  unsurpassed  model.  And  indeed 
the  most  enthusiastic  admiration  of  this  wonderful  organ 
is  only  natural,  when  we  consider  what  functions  it  per- 
forms ;  when  we  dwell  on  its  penetrating  power,  on  the 
swiftness  of  succession  of  its  brilliant  pictures,  and  on 
the  riches  which  it  spreads  before  our  sense.  It  is  by 
the  eye  alone  that  we  know  the  countless  shining  worlds 
that  fill  immeasurable  space,  the  distant  landscapes  of 
our  own  earth,  with  all  the  varieties  of  sunlight  that 
reveal  them,  the  wealth  of  form  and  colour  among 
flowers,  the  strong  and  happy  life  that  moves  in  animals. 
Next  to  the  loss  of  life  itself  that  of  eyesight  is  the 
heaviest. 

But  even  more  important,  than  the  delight  in  beauty 
and  admiration  of  majesty  in  the  creation  which  we  owe 
to  the  eye,  is  the  security  and  exactness  with  Avhich  we 
can  judge  by  sight  of  the  position,  distance,  and  size  of 
tlie  objects  which  surround  us.  For  this  knowledge  is 
the  necessary  foundation  for  all  our  actions,  from  thread- 
ing a  needle  through  a  tangled  skein  of  silk  to  leaping 
from  cliff  to   cliff  when  life  itself  depends  on  the  right 


202   RECENT   PROGRESS   OF   THE .  THEORY   OF   VISION. 

measurement  of  the  distance.  In  fact,  the  success  of 
the  movements  and  actions  dependent  on  the  accuracy 
of  the  pictures  that  the  eye  gives  us  forms  a  con- 
tinual test  and  confirmation  of  that  accuracy.  If  sight 
were  to  deceive  us  as  to  the  position  and  distance  of 
external  objects,  we  should  at  once  become  aware  of  the 
delusion  on  attempting  to  grasp  or  to  approach  them. 
This  daily  verification  by  our  other  senses  of  the  im- 
pressions we  receive  by  sight  produces  so  firm  a  conviction 
of  its  absolute  and  complete  truth  that  the  exceptions 
taken  by  philosophy  or  physiology,  however  well  grounded 
they  may  seem,  have  no  power  to  shake  it. 

No  wonder  then  that,  according  to  a  wide-spread  con- 
viction, the  eye  is  looked  on  as  an  optical  instrument 
so  perfect  that  none  formed  by  human  hands  can  ever 
be  compared  with  it,  and  that  its  exact  and  complicated 
construction  should  be  regarded  as  the  full  explanation 
of  the  accuracy  and  variety  of  its  functions. 

Actual  examination  of  the  performances  of  the  eye  as 
an  optical  instrument  carried  on  chiefly  during  the  last 
ten  years  has  brought  about  a  remarkable  change  in  these 
views,  just  as  in  so  many  other  cases  the  test  of  facts 
has  disabused  our  minds  of  similar  fancies.  But  as  again 
in  similar  cases  reasonable  admiration  rather  increases 
than  diminishes  when  really  important  functions  are 
more  clearly  understood  and  their  object  better  esti- 
mated, so  it  may  well  be  with  our  more  exact  knowledge 
of  the  eye.  For  the  great  performances  of  this  little 
organ  can  never  be  denied ;  and  while  we  might  con- 
sider ourselves  compelled  to  withdraw  our  admiration 
from  one  point  of  view,  we  must  again  experience  it 
from  another. 

Regarded  as  an  optical  instrument,  the  eye  is  a  camera 
obscura.  This  apparatus  is  well  known  in  the  form  used 
by  photographers  (Fig.  27).     A  box  constructed  of  two 


THE   EYE   AS   AN   OPTICAL    INSTRUMENT. 


203 


parts,  of  which  one  slides  in  the  otlier,  and  blackened, 
has  in  front  a  combination  of  lenses  fixed  in  the  tube 
h  i  on  the  inside,  which  refract  the  incident  rays  of  light, 
and  unite  them  at  the  back  of  the  instrument  into  an 
optical  image  of  the  objects  which  lie  in  front  of  the 
camera.  When  the  photographer  first  arranges  his  instru- 
ment, he  receives  the  image  upon  a  plate  of  ground  glass, 
g.  It  is  there  seen  as  a  small  and  elaborate  picture  in 
its  natural  colours,  more  clear  and  beautiful  than  tlie 
most  skilful  painter  could  imitate,  tliough  indeed  it  is 
upside  down.     The  next  step  is  to  substitute  for   this 


Iw.  27. 

glass  a  prepared  plate  upon  which  the  light  exerts  a  per- 
manent chemical  effect,  stronger  on  the  more  brightly 
illuminated  parts,  weaker  on  those  which  are  darker. 
These  chemical  changes  having  once  taken  place  are  per- 
manent :  by  their  means  the  image  is  fixed  upon  the  plate. 
The  natural  camera  obscura  of  the  eye  (seen  in  a 
diagrammatic  section  in  Fig.  28)  has  its  blackened 
chamber  globular  instead  of  cubical,  and  made  not  of 
wood,  but  of  a  thick,  strong,  white  substance  known  as  the 
sclerotic  coat.  It  is  this  which  is  partly  seen  between 
10 


204   RECEXT   PROGRESS    OF   THE   THEORY   OP   VISION. 

the  eyelids  as  'the  white  of  the  eye.'  This  globular 
chamber  is  lined  with  a  delicate  coat  of  winding  blood- 
vessels covered  inside  by  black  pigment.  But  the  apple 
of  the  eye  is  not  empty  like  the  camera :  it  is  filled  with 
a  transparent  jelly  as  clear  as  water.  The  lens  of  the 
camera  obscura  is  represented,  first,  by  a  convex  trans- 
parent window  like  a  pane  of  horn  (the  cornea),  which 
is  fixed  in  front  of  the  sclerotic  like  a  watch  glass  in  front 


of  its  metal  case.  This  union  and  its  own  firm  texture 
make  its  position  and  its  curvature  constant.  But  the 
glass  lenses  of  the  photographer  are  not  fixed ;  they  are 
moveable  by  means  of  a  sliding  tube  which  can  be  ad- 
justed by  a  screw  (Fig.  27,  r),  so  as  to  bring  the  objects 
in  front  of  the  camera  into  focus.  The  nearer  they  are, 
the  farther  the  lens  is  pushed  forward ;  tlie  farther  off, 
the  more  it  is  screwed  in.  The  eye  has  the  same  task 
of  bringing  at  one  time  near,  at  another  distant,  objects  to 
a  focus  at  the  back  of  its  dark  chamber.     So  that  some 


THE   EYE   AS   AN   OPTICAL   INSTRUMENT.  205 

power  of  adjustment  or  'accommodation'  is  necessary. 
This  is  accomplished  by  the  movements  of  the  crystalline 
lens  (Fig.  28,  L),  which  is  placed  a  short  distance  behind 
the  cornea.  It  is  covered  by  a  curtain  of  varying  colour, 
the  iris  (J),  which  is  perforated  in  the  centre  by  a  round 
hole,  the  pupil,  the  edges  of  which  are  in  contact  with  the 
front  of  the  lens.  Through  this  opening  we  see  through 
the  transparent  and,  of  course,  invisible  lens  the  black 
chamber  within.  The  crystalline  lens  is  circular,  bi- 
convex, and  elastic.  It  is  attached  at  its  edge  to  the 
inside  of  the  eye  by  means  of  a  circular  band  of  folded 
membrane  which  surrounds  it  like  a  plaited  ruff,  and 
is  called  the  ciliary  body  or  Zonule  of  Zinn  (Fig. 
28,  *  ■^).  The  tension  of  this  ring  (and  so  of  the  lens 
itself)  is  regulated  by  a  series  of  muscular  fibres  known 
as  the  ciliary  muscle  (Cc).  When  this  muscle  con- 
tracts, the  tension  of  the  lens  is  diminished,  and  its  sur- 
faces— but  chiefly  the  front  one — become  by  its  physical 
property  of  elasticity  more  convex  than  when  the  eye 
is  at  rest ;  its  refractive  power  is  thus  increased,  and  the 
images  of  near  objects  are  brought  to  a  focus  on  the  back 
of  the  dark  chamber  of  the  eye. 

Accordingly  the  healthy  eye  when  at  rest  sees  distant 
objects  distinctly :  by  the  contraction  of  the  ciliary 
muscle  it  is  'accommodated'  for  those  which  are  near. 
The  mechanism  by  which  this  is  accomplished,  as  above 
shortly  explained,  was  one  of  the  greatest  riddles  of  the 
physiology  of  the  eye  since  the  time  of  Kepler ;  and  the 
knowledge  of  its  mode  of  action  is  of  the  greatest  prac- 
tical importance  from  the  frequency  of  defects  in  the 
power  of  accommodation.  No  problem  in  optics  has 
given  rise  to  so  many  contradictory  theories  as  this.  The 
key  to  its  solution  was  found  when  the  French  surgeon 
Sanson  first  observed  very  faint  reflexions  of  light  through 
the  pupil  from  the  two  surfaces  of  the  crystalline  lens, 


206   KECENT   PEOGRESS   OF   TPIE   THEORY   OF   VISION. 

and  thus  acquired  the  character  of  an  unusually  careful 
observer.  For  this  phenomenon  was  anything  but  ob- 
vious ;  it  can  only  be  seen  by  strong  side  illumination, 
in  darkness  otherwise  complete,  only  when  the  observer 
takes  a  certain  position,  and  then  all  he  sees  is  a  faint 
misty  reflexion.  But  this  faint  reflexion  was  destined 
to  become  a  shining  light  in  a  dark  corner  of  science.  It 
was  in  fact  the  first  appearance  observ^ed  in  the  living 
eye  which  came  directly  from  the  lens.  Sanson  imme- 
diately applied  his  discovery  to  ascertain  whether  the 
lens  was  in  its  place  in  cases  of  impaired  vision.  Max 
Langenbeck  made  the  next  step  by  observing  that  the 
reflexions  from  the  lens  alter  during  accommodation. 
These  alterations  were  employed  by  Cramer  of  Utrecht, 
and  also  independently  by  the  present  writer,  to  arrive 
at  an  exact  knowledge  of  all  the  changes  which  the  lens 
undergoes  during  the  process  of  accommodation.  I  suc- 
ceeded in  applying  to  the  moveable  eye  in  a  modified 
form  the  principle  of  the  heliometer,  an  instrument  by 
which  astronomers  are  able  so  accurately  to  measure  small 
distances  between  stars  in  spite  of  their  constant  apparent 
motion  in  the  heavens,  that  they  can  thus  sound  the 
depths  of  the  region  of  the  fixed  stars.  An  instrument  con- 
structed for  the  purpose,  the  ophthalmometer,  enables 
us  to  measure  in  the  living  eye  the  curvature  of  the 
cornea,  and  of  the  two  surfaces  of  the  lens,  the  distance 
of  these  from  each  other,  &c.,  with  greater  precision 
than  could  before  be  done  even  after  death.  By  this 
means  we  can  ascertain  the  entire  range  of  the  changes 
of  the  optical  apparatus  of  the  eye  so  far  as  it  affects 
accommodation. 

The  physiological  problem  was  therefore  solved.  Ocu- 
lists, and  especially  Donders,  next  investigated  the  indi- 
vidual defects  of  accommodation  which  give  rise  to  the 
conditions  known  as  long  sight  and  short  sight.     It  was 


THE   EYE   AS   AN   OPTICAL    INSTRUMENT.  207 

necessary  to  devise  trustworthy  raethods  in  order  to 
ascertain  the  precise  limits  of  the  power  of  accommoda- 
tion even  with  inexperienced  and  uninstructed  patients. 
It  became  apparent  that  very  different  conditions  had 
been  confounded  as  short  sight  and  long  sight,  and  this 
confusion  bad  made  the  choice  of  suitable  glasses  un- 
certain. It  was  also  discovered  that  some  of  the  most 
obstinate  and  obscure  aflfections  of  the  sight,  formerly 
reputed  to  be  'nervous,'  simply  depended  on  certain 
defects  of  accommodation,  and  could  be  readily  removed 
by  using  suitable  glasses.  Moreover  Donders  *  proved 
that  the  same  defects  of  accommodation  are  the  most 
frequent  cause  of  squinting,  and  Von  Grraefe*  had  already 
shown  that  neglected  and  progressive  shortsightedness 
tends  to  produce  the  most  dangerous  expansion  and 
deformity  of  the  back  of  the  globe  of  the  eye. 

Thus  connections  were  discovered,  where  least  expected, 
between  the  optical  discovery  and  important  diseases, 
and  the  result  was  no  less  beneficial  to  the  patient  than 
interesting  to  the  physiologist. 

We  must  now  speak  of  the  curtain  which  receives  the 
optical  image  when  brought  to  a  focus  in  the  eye.  This 
is  the  retina,  a  thin  membranous  expansion  of  the  optic 
nerve  which  forms  the  innermost  of  the  coats  of  the  eye. 
The  optic  nerve  (Fig.  2,  0)  is  a  cylindrical  cord  which 
contains  a  multitude  of  minute  fibres  protected  by  a 
strong  tendinous  sheath.  The  nerve  enters  the  apple  of 
the  eye  from  behind,  rather  to  the  inner  (nasal)  side  of 
the  middle  of  its  posterior  hemisphere.  Its  fibres  then 
spread  out  in  all  directions  over  the  front  of  the  retina. 
They  end  by  becoming  connected,  first,  with  ganglion  cells 
and  nuclei,  like  those  found  in  the  brain ;  and,  secondly, 

•  Professor  of  Physiology  in  the  University  of  Utrecht. 

'  This  great  ophthahnic  surgeon  died  in  Berlin  at  the  early  age  of  forty-two. 


208   EECENT   PROGRESS    OF   THE   THEORY   OF   VISION. 

with  structures  not  elsewhere  found,  called  rods  and  cones. 
The  rods  are  slender  cylinders ;  the  cones,  or  bulbs,  some- 
wliat  thicker,  flask- shaped  structures.  All  are  ranged 
perpendicular  to  the  surface  of  the  retina,  closely  packed 
together,  so  as  to  form  a  regular  mosaic  layer  behind  it. 
Each  rod  is  connected  with  one  of  the  minutest  nerve 
fibres,  each  cone  with  one  somewhat  thicker.  This  layer 
of  rods  and  bulbs  (also  known  as  membrana  Jacobi)  has 
been  proved  by  direct  experiments  to  be  the  really  sensi- 
tive layer  of  the  retina,  the  structure  in  which  alone 
the  action  of  light  is  capable  of  producing  a  nervous 
excitation. 

There  is  in  the  retina  a  remarkable  spot  which  is  placed 
near  its  centre,  a  little  to  the  outer  (temporal)  side,  and 
which  from  its  colour  is  called  the  yellow  spot.  The 
retina  is  here  somewhat  thickened,  but  in  the  middle  of 
the  yellow  spot  is  found  a  depression,  the  fovea  centrcdis, 
where  the  retina  is  reduced  to  those  elements  alone  which 
are  absolutely  necessary  for  exact  vision.  Fig.  29,  from 
Henle,  shows  a  thin  transverse  section  of  this  central  de- 
pression made  on  a  retina  which  had  been  hardened  in 
alcohol.  Lh  {Lamina  hyalina,  membrana  limitans)  is 
an  elastic  membrane  which  divides  the  retina  from  the 
vitreous.  The  bulbs  (seen  at  6)  are  here  smaller  than 
elsewhere,  measuring  only  the  400th  part  of  a  millimeter 
in  diameter,  and  form  a  close  and  regular  mosaic.  The 
other,  more  or  less  opaque,  elements  of  the  retina  are 
seen  to  be  wanting,  except  the  corpuscles  (^),  which 
belong  to  the  cones.  At/  are  seen  the  fibres  which  unite 
these  with  the  rest  of  the  retina.  This  consists  of  a  layer 
of  fibres  of  the  optic  nerve  {n)  in  front,  and  two  layers  of 
nerve  cells  {gli  and  gle\  known  as  the  internal  and  exter- 
nal ganglion  layers,  with  a  stratum  of  fine  granules  (gri) 
between  them.  All  these  parts  of  the  retina  are  absent 
at  the  bottom  of  the  fovea  centralis,  and  their  gradual 


THE   EYE   AS   AN   OPTICAL    INSTRUMENT. 


209 


thinning  away  at  its  borders  is  seen  in  the  diagram.  Nor 
do  the  bli;od  vessels  of  the  retina  enter  the  fovea^  but  end 
in  a  circle  of  delicate  capillaries  around  it. 


^        %Si 


This  fovea,  or  pit  of  the  retina,  is  of  great  importance 
for  vision,  since  it  is  the  spot  where  the  most  exact  dis- 


210   KECENT   PROGRESS    OF   THE   THEORY   OF   VISION". 

crimination  of  distances  is  made.  The  cones  are  here 
packed  most  closely  together,  and  receive  light  which  has 
not  been  impeded  by  other  semi-transparent  parts  of  the 
retina.  We  may  assume  that  a  single  nervous  fibril  runs 
from  each  of  these  cones  through  the  trunk  of  the  optic 
nerve  to  the  brain,  without  touching  its  neighbours,  and 
there  produces  its  special  impression,  so  that  the  excita- 
tion of  each  individual  cone  will  produce  a  distinct  and 
separate  effect  upon  the  sense. 

The  production  of  optical  images  in  a  camera  obscura 
depends  on  the  well-known  fact  that  the  rays  of  light 
which  come  off  from  an  illuminated  object  are  so  broken  or 
refracted  in  passing  through  the  lenses  of  the  instrument, 
that  they  follow  new  directions  which  bring  them  all  to  a 
single  point,  the  focus,  at  the  back  of  the  camera.  A  com- 
mon burning  glass  has  the  same  property ;  if  we  allow  the 
rays  of  the  sun  to  pass  through  it,  and  hold  a  sheet  of  white 
paper  at  the  proper  distance  behind  it,  we  may  notice  two 
eifects.  In  the  first  place  (and  this  is  often  disregarded) 
the  burning  lens,  although  made  of  transparent  glass, 
throws  a  shadow  like  any  opaque  body  ;  and  next  we  see 
in  the  middle  of  this  shadow  a  spot  of  dazzling  brilliance, 
the  image  of  the  sun.  The  rays  which,  if  the  lens  had 
not  been  there,  would  have  illuminated  the  whole  space 
occupied  by  the  shadow,  are  concentrated  by  the  refracting 
power  of  the  burning  glass  upon  the  bright  spot  in  the 
middle,  and  so  both  light  and  heat  are  more  intense  there 
than  where  the  unrefracted  solar  rays  fall.  If,  instead  of 
the  disc  of  the  sun,  we  choose  a  star  or  any  other  point  as 
the  source  of  light,  its  light  will  be  united  into  a  point  at 
the  focus  of  the  lens,  and  the  image  of  the  star  will  appear 
as  such  upon  the  white  paper.  If  there  is  another  fixed 
star  near  the  one  first  chosen,  its  light  will  be  collected  at 
a  second  illuminated  point  on  the  paper;  and  if  the  star 


THE  EYE  AS   AN   OPTICAL   INSTRUMENT.  211 

happen  to  send  out  red  rays,  its  image  on  the  paper  will 
also  appear  red.  The  same  will  be  true  of  any  number 
of  neighbouring  stars,  the  image  of  each  corresponding 
to  it  in  brilliance,  colour,  and  relative  position.  And  if, 
instead  of  a  multitude  of  separate  luminous  points,  we 
have  a  continuous  series  of  them  in  a  bright  line  or  sur- 
face, a  similar  line  or  surface  will  be  produced  upon  the 
paper.  But  here  also,  if  the  piece  of  paper  be  put  to  the 
proper  distance,  all  the  light  that  proceeds  from  any  one 
point  will  be  brought  to  a  focus  at  a  point  which  corre- 
sponds to  it  in  strength  and  colour  of  illumination,  and 
(as  a  corollary)  no  point  of  the  paper  receives  light  from 
more  than  a  single  point  of  the  object. 

If  now  we  replace  our  sheet  of  white  paper  by  a  pre- 
pared photographic  plate,  each  point  of  its  surface  will  be 
altered  by  the  light  which  is  concentrated  on  it.  This 
light  is  all  derived  from  the  corresponding  point  in  the 
object,  and  answers  to  it  in  intensity.  Hence  the  changes 
which  take  place  on  the  plate  will  correspond  in  amount 
to  the  chemical  intensity  of  the  rays  which  fall  upon  it. 

This  is  exactly  what  takes  place  in  the  eye.  Instead 
of  the  burning  glass  we  have  the  cornea  and  crystalline 
lens  ;  and  instead  of  the  piece  of  paper,  the  retina.  Accord- 
ingly, if  an  optically  accurate  image  is  thrown  upon  the 
retina,  each  of  its  cones  will  be  reached  by  exactly  so 
much  light  as  proceeds  from  the  corresponding  point  in 
the  field  of  vision ;  and  also  the  nerve  fibre  which  arises 
from  each  cone  will  be  excited  only  by  the  light  proceeding 
from  the  corresponding  point  in  the  field,  while  other 
nerve  fibres  will  be  excited  by  the  light  proceeding  from 
other  points  of  the  field.  P'ig.  30  illustrates  tliis  effect. 
Tlie  rays  which  come  from  the  point  A  in  the  object  of 
vision  are  so  broken  that  they  all  unite  at  a  on  the  retina, 
while  those  from  B  unite  at  h.  Thus  it  results  that  the 
light  of  each  separate  bright  point  of  the  field  of  vision 


212   EECEXT   PROGRESS    OF   THE   THEORY   OP   VISION. 

excites  a  separate  impression ;  that  the  difference  of  the 
several  points  of  the  field  of  vision  in  degree  of  brightness 
can  be  appreciated  by  the  sense  ;  and  lastly,  that  separate 
impressions  may  each  arrive  separately  at  the  seat  of 
consciousness. 

If  now  we  compare  the  eye  with  other  optical  instru- 
ments, we  observe  the  advantage  it  has  over  them  in  its 
very  large  field  of  vision.  This  for  each  eye  separately  is 
160°  (nearly  two  right  angles)  laterally,  and  120°  verti- 
cally, and  for  both  together  somewhat  more  than  two 
right  angles  from  right  to  left.     The  field  of  view  of  in- 


FiG.  30. 

struments  made  by  art  is  usually  very  small,  and  becomes 
smaller  with  the  increased  size  of  the  image. 

But  we  must  also  admit,  that  we  are  accustomed  to 
expect  in  these  instruments  complete  precision  of  the 
image  in  its  entire  extent,  while  it  is  only  necessary  for 
the  image  on  the  retina  to  be  exact  over  a  very  small 
surface,  namely,  that  of  the  yellow  spot.  The  diameter 
of  the  central  pit  corresponds  in  the  field  of  vision  to  an 
angular  magnitude  which  can  be  covered  by  the  nail  of 
one's  forefinger  when  the  hand  is  stretched  out  as  far  as 
possible.  In  this  small  part  of  the  field  our  power  of 
vision  is  so  accurate  that  it  can  distinguish  the  distance 
between  two  points,  of  only  one  minute  angular  magni- 
tude, i.e.  a  distance  equal  to  the  sixtieth  part  of  the 
diameter  of  the  finger-nail.     This  distance  corresponds  to 


THE  EYE  AS   AN  OPTICAL   INSTRUMENT.  213 

the  width  of  one  of  the  cones  of  the  retina.  All  the  other 
parts  of  the  retinal  image  are  seen  imperfectly,  and  the 
more  so  the  nearer  to  the  limit  of  the  retina  they  fall. 
So  that  the  image  which  we  receive  by  the  eye  is  like  a 
picture,  minutely  and  elaborately  finished  in  the  centre, 
but  only  roughly  sketched  in  at  the  borders.  But  although 
at  each  instant  we  only  see  a  very  small  part  of  the  field 
of  vision  accurately,  we  see  this  in  combination  with 
what  surrounds  it,  and  enough  of  this  outer  and  larger 
part  of  the  field,  to  notice  any  striking  object,  and  parti- 
cularly any  change  that  takes  place  in  it.  All  of  this  is 
unattainable  in  a  telescope. 

But  if  the  objects  are  too  small,  we  cannot  discern 
them  at  all  with  the  greater  part  of  the  retina. 

When,  lost  in  boundless  blue  on  high, 
The  lark  pours  forth  his  thrilling  song,* 

the  '  ethereal  minstrel '  is  lost  until  we  can  bring  her 
image  to  a  focus  upon  the  central  pit  of  our  retina. 
Then  only  are  we  able  to  see  her. 

To  look  at  anything  means  to  place  the  eye  in  such  a  po- 
sition that  the  image  of  the  object  falls  on  the  small  region 
of  perfectly  clear  vision.  This  we  may  call  direct  vision, 
applying  the  term  indirect  to  that  exercised  with  the 
lateral  parts  of  the  retina — indeed  with  all  except  the 
yellow  spot. 

The  defects  which  result  from  the  inexactness  of  vision 
and  the  smaller  number  of  cones  in  the  greater  part  of 
the  retina  are  compensated  by  the  rapidity  with  which  we 
can  turn  the  eye  to  one  point  after  another  of  the  field 
of  vision,  and   it   is   this  rapidity  of  movement  which 

'  The  lines  in  the  well-known  passage  of  Faust : — 

"Wenn  iiber  uns  im  blauen  Eaum  rerloren 
Ihr  schmetternd  Lied  die  Lerche  singt. 


214   RECEXT   PROGRESS   OF  THE   THEORY   OP  VISION. 

really  constitutes  the  chief  advantage  of  the  eye  over 
other  optical  instruments. 

Indeed  the  peculiar  way  in  which  we  are  accustomed 
to  give  our  attention  to  external  objects,  by  turning  it 
only  to  one  thing  at  a  time,  and  as  soon  as  this  has  been 
taken  in  hastening  to  another,  enables  the  sense  of  vision 
to  accomplish  as  much  as  is  necessary  ;  and  so  we  have 
practically  the  same  advantage  as  if  we  enjoyed  an  accu- 
rate view  of  the  whole  field  of  vision  at  once.  It  is  not  in 
tact  until  we  begin  to  examine  our  sensations  closely  that 
we  become  aware  of  the  imperfections  of  indirect  vision. 
Whatever  we  want  to  see  we  look  at,  and  see  it  accurately  ; 
what  we  do  not  look  at,  we  do  not  as  a  rule  care  for  at 
the  moment,  and  so  do  not  notice  how  imperfectly  we 
see  it. 

Indeed,  it  is  only  after  long  practice  that  we  are 
able  to  turn  our  attention  to  an  object  in  the  field  of 
indirect  vision  (as  is  necessary  for  some  physiological 
observations)  without  looking  at  it,  and  so  bringing  it 
into  direct  view.  And  it  is  just  as  difficult  to  fix  the 
eye  on  an  object  for  the  number  of  seconds  required  to 
produce  the  phenomenon  of  an  after-image.*  To  get 
this  well  defined  requires  a  good  deal  of  practice. 

A  great  part  of  the  importance  of  the  eye  as  an  organ 
of  expression  depends  on  the  same  fact ;  for  the  move- 
ments of  the  eyeball — its  glances — are  among  the  most 
direct  signs  of  the  movement  of  the  attention,  of  the 
movements  of  the  mind,  of  the  person  who  is  looking 
at  us. 

Just  as  quickly  as  the  eye  turns  upwards,  downwards, 
and  from  side  to  side,  does  the  accommodation  change, 
so  as  to  bring  the  object  to  which  our  attention  is  at 
the  moment  directed  into  focus ;  and  thus  near  and  dis- 
tant objects  pass  in  rapid  succession  into  accurate  view. 

'  Vide  infra,  p.  254. 


THE   EYE   AS  AN   OPTICAL   INSTRUMENT.  215 

All  these  changes  of  direction  and  of  accommodation 
take  place  far  more  slowly  in  artificial  instruments.  A 
photographic  camera  can  never  show  near  and  distant 
objects  clearly  at  once,  nor  can  the  eye ;  but  the  eye 
shows  them  so  rapidly  one  after  another  that  most  people, 
who  have  not  thought  how  they  see,  do  not  know  that 
there  is  any  change  at  all. 

Let  us  now  examine  the  optical  properties  of  the  eye 
further*  We  will  pass  over  the  individual  defects  of 
accommodation  which  have  been  already  mentioned  as 
the  cause  of  short  and  long  sight.  These  defects  appear 
to  be  partly  the  result  of  our  artificial  way  of  life,  partly 
of  the  changes  of  old  age.  Elderly  persons  lose  their 
power  of  accommodation,  and  their  range  of  clear  vision 
becomes  confined  within  more  or  less  narrow  limits.  To . 
exceed  these  they  must  resort  to  the  aid  of  glasses. 

But  there  is  another  quality  which  we  expect  of  optical 
instruments,  namely,  that  they  shall  be  free  from  disper- 
sion— that  they  be  achromatic.  Dispersion  of  light  de- 
pends on  the  fact  that  the  coloured  rays  which  united 
make  up  the  white  light  of  the  sun  are  not  refracted  in 
exactly  the  same  degree  by  any  transparent  substance 
known.  Hence  the  size  and  position  of  the  optical 
images  thrown  by  these  differently  coloured  rays  are  not 
''^It^  the  same  ;  they  do  not  perfectly  overlap  each  other 
in  the  field  of  vision,  and  thus  the  white  surface  of  the 
image  appears  fringedwith  a  violet  or  orange,  according 
as  the  red  or  blue  rays  are  broader.  This  of  course  takes 
off  so  far  from  the  sharpness  of  the  outline. 

Many  of  my  readers  know  what  a  curious  part  the 
inquiry  into  the  chromatic  dispersion  of  the  eye  has 
played  in  the  invention  of  achromatic  telescopes.  It  is 
a  celebrated  instance  of  how  a  right  conclusion  may 
sometimes  be  drawn  from  two  false  premisses.     Newton 


216   RECENT   PHOGRESS   OF   THE   THEORY   OP  VISIOJT. 

thought  he  had  discovered  a  relation  between  the  re- 
fractive and  dispersive  powers  of  various  transparent 
materials,  from  which  it  followed  that  no  achromatic 
refraction  was  possible.  Euler,'  on  the  other  hand,  con- 
cluded that,  since  the  eye  is  achromatic,  the  relation 
discovered  by  Newton  could  not  be  correct.  Keasoning 
from  this  assumption,  he  constructed  theoretical  rules 
for  making  achromatic  instruments,  and  Dolland  ^  carried 
them  out.  But  Dolland  himself  observed  that  the  eye 
could  not  be  achromatic,  because  its  construction  did  not 
answer  to  Euler's  rules ;  and  at  last  Fraunhofer^  actually 
measured  the  degree  of  chromatic  aberration  of  the  eye. 
An  eye  constructed  to  bring  red  light  from  infinite  dis- 
tance to  a  focus  on  the  retina  can  only  do  the  same  with 
violet  rays  from  a  distance  of  two  feet.  AYith  ordinary 
light  this  is  not  noticed  because  these  extreme  colours  are 
the  least  luminous  of  all,  and  so  the  images  they  produce 
are  scarcely  observed  beside  the  more  intense  images  of 
the  intermediate  yellow,  green,  and  blue  rays.  But  the 
effect  is  very  striking  when  we  isolate  the  extreme  rays 
of  the  spectrum  by  means  of  violet  glass.  Glasses 
coloured  with  cobalt  oxide  allow  the  red  and  blue  rays 
to  pass,  but  stop  the  green  and  yellow  ones,  that  is,  the 
brightest  rays  of  the  spectrum.  If  those  of  my  readers 
who  have  eyes  of  ordinary  focal  distance  will  look  at 
lighted  street  lamps  from  a  distance  with  this  violet 
glass,  they  will  see  a  red  flame  surrounded  by  a  broad 
bluish  violet  halo.  This  is  the  dispersive  image  of  the 
flame  thrown  by  its  blue  and  violet  light.  The  phe- 
nomenon is  a  simple  and  complete  proof  of  the  fact  of 
chromatic  aberration  in  the  eye. 

Now  the  reason  why  this  defect  is  so  little  noticed 

'  Leonard  Euler  born  at  Basel,  1707  ;  died  at  St.  Petersburgh,  1783. 

2  John  Dolland,  F.R.S.  born  1706  ;  died  in  London,  1761. 

'  Joseph  Fraunhofer  born  in  Bararia,  1787 ;  died  at  Munich,  1826. 


THE   EYE  AS  AN   OPTICAL   INSTRUMENT.  217 

under  ordinary  circumstances,  and  why  it  is  in  fact 
somewhat  less  than  a  glass  instrument  of  the  same 
construction  would  have,  is  that  the  chief  refractive 
medium  of  the  eye  is  water,  which  possesses  a  less  dis- 
persive power  than  glass.  ^  Hence  it  is  that  the  chro- 
matic aberration  of  the  eye,  though  present,  does  not 
materially  affect  vision  with  ordinary  white  illumination. 

A  second  defect  which  is  of  great  importance  in  optical 
instruments  of  high  magnifying  power  is  what  is  known 
as  spherical  aberration.  Spherical  refracting  surfiices 
approximately  unite  the  rays  which  proceed  from  a  lumin- 
ous point  into  a  single  focus,  only  when  each  ray  falls 
nearly  perpendicularly  upon  the  corresponding  part  of 
the  refracting  surface.  If  all  those  rays  which  form  the 
centre  of  the  image  are  to  be  exactly  united,  a  lens  with 
other  than  spherical  surfaces  must  be  used,  and  this 
cannot  be  made  with  sufficient  mechanical  perfection. 
Now  the  eye  has  its  refracting  surfaces  partly  elliptical ; 
and  so  here  again  the  natural  prejudice  in  its  favour  led 
to  the  erroneous  belief  that  spherical  aberration  was  thus 
prevented.  But  this  was  a  still  greater  blunder.  More 
accurate  investigation  showed  that  much  greater  defects 
than  that  of  spherical  aberration  are  present  in  the  eye, 
defects  which  are  easily  avoided  with  a  little  care  in 
making  optical  instruments,  and  compared  with  which 
the  amount  of  spherical  aberration  becomes  very  unim- 
portant. The  careful  measurements  of  the  curvature  of  the 
cornea,  first  made  by  Senff  of  Dorpat,  next,  with  a  better 
adapted  instrument,  the  writer's  ophthalmometer  already 
referred  to,  and  afterwards  carried  out  in  numerous 
cases  by  Bonders,  Knapp,  and  others,  have  proved  that 
the  cornea  of  most  human  eyes  is  not  a  perfectly  sym- 

'  But  still  the  diffraction  in  the  eye  is  rather  greater  than  an  instrument 
made  with  water  would  produce  under  the  same  conditions. 


218   RECEXT   PROGRESS   OF   THE  THEORY  OF  VISION. 

metrical  curve,  but  is  variously  bent  in  differfjnt  direc- 
tions. I  have  also  devised  a  method  of  testing  the 
*  centering '  of  an  eye  during  life,  i.e.  ascertaining  whether 
the  cornea  and  the  crystalline  lens  are  symmetrically 
placed  with  regard  to  their  common  axis.  By  this  means 
I  discovered  in  the  eyes  I  examined  slight  but  distinct 
deviations  from  accurate  centering.  The  result  of  these 
two  defects  of  construction  is  the  condition  called  astig- 
viatism,  which  is  found  more  or  less  in  most  human  eyes, 
and  prevents  our  seeing  vertical  and  horizontal  lines  at 
the  same  distance  perfectly  clearly  at  once.  If  the  degree 
of  astigmatism  is  excessive,  it  can  be  obviated  by  the  use 
of  glasses  with  cylindrical  surfaces,  a  circumstance  which 
has  lately  much  attracted  the  attention  of  oculists. 

Nor  is  this  all.  A  refracting  surface  which  is  im- 
perfectly elliptical,  an  ill-centered  telescope,  does  not 
give  a  single  illuminated  point  as  the   image  of  a  star, 


Fre.  31. 


but,  according  to  the  surface  and  arrangement  of  the 
refracting  media,  elliptic,  circular,  or  linear  images.  Now 
the  images  of  an  illuminated  point,  as  the  human  eye 
brings  tliem  to  focus,  are  even  more  inaccurate :  they  are 
irregularly  radiated.     The  reason  of  this  lies  in  the  con- 


THE   EYE   AS   AN   OPTICAL   INSTRUMENT.  219 

st ruction  of  the  crystalline  lens,  the  fibres  of  which  are 
arranged  around  six  diverging  axes  (shown  in  Fig.  31).  So 
that  the  rays  which  we  see  around  stars  and  other  distant 
liphts  are  imaees  of  the  radiated  structure  of  our  lens  ; 
and  the  universality  of  this  optical  defect  is  proved  by  any 
figure  with  diverging  rays  being  called  '  star-shaped.'  It 
is  from  the  same  cause  that  the  moon,  while  her  crescent 
is  still  narrow,  appears  to  many  persons  double  or  three- 
fold. 

Now  it  is  not  too  much  to  say  that  if  an  optician 
wanted  to  sell  me  an  instrument  which  had  all  these 
defects,  I  should  think  myself  quite  justified  in  blaming 
his  carelessness  in  the  strongest  terms,  and  giving  him 
back  his  instrument.  Of  course,  I  shall  not  do  this  with 
my  eyes,  and  shall  be  only  too  glad  to  keep  them  as  long 
as  I  can — defects  and  all.  Still,  the  fact  that,  however 
bad  they  may  be,  I  can  get  no  others,  does  not  at  all 
diminish  their  defects,  so  long  as  I  maintain  the  narrow 
but  indisputable  position  of  a  critic  on  purely  optical 
grounds. 

We  have,  however,  not  yet  done  with  the  list  of  the 
defects  of  the  eye. 

We  expect  that  the  optician  will  use  good,  clear,  per- 
fectly transparent  glass  for  his  lenses.  If  it  is  not  so, 
a  bright  halo  will  appear  around  each  illuminated  surface 
in  the  image:  what  should  be  black  looks  grey,  what 
should  be  white  is  dull.  But  this  is  just  what  occurs 
in  the  image  our  eyes  give  us  of  the  outer  world.  The 
obscurity  of  dark  objects  when  seen  near  very  bright  ones 
depends  essentially  on  this  defect;  and  if  we  throw  a 
strong  light  ^  through  the  cornea  and  crystalline  lens, 
they  appear  of  a  dingy  white,  less  transparent  than  the 
'  aqueous  humour  '  which  lies  between  them.  This  defect 
*  Eg.  from  a  lamp,  concentrated  by  a  bull's-eye  condenser. 


220   RECENT   PROGEESS   OF   THE   THEORY   OF   YISIOIS-. 

is  most  apparent  in  the  blue  and  violet  rays  of  the  solar 
spectrum  ;  for  there  comes  in  the  phenomenon  of  fluo- 
rescence ^  to  increase  it. 

In  fact,  although  the  crystalline  lens  looks  so  beauti- 
fully clear  when  taken  out  of  the  eye  of  an  animal  just 
killed,  it  is  far  from  optically  uniform  in  structure.  It 
is  possible  to  see  the  shadows  and  dark  spots  within  the 
eye  (the  so-called  '  entoptic  objects ')  by  looking  at  an 
extensive  bright  surface — the  clear  sky,  for  instance — 
through  a  very  narrow  opening.  And  these  shadows  are 
chiefly  due  to  the  fibres  and  spots  in  the  lens. 

There  are  also  a  number  of  minute  fibres,  corpuscles 
and  folds  of  membrane,  which  float  in  the  vitreous 
humour,  and  are  seen  when  they  come  close  in  front 
of  the  retina,  even  under  the  ordinary  conditions  of 
vision.  They  are  then  called  muscce  volitantes,  because 
when  the  observer  tries  to  look^  at  them,  they  naturally  move 
with  the  movement  of  the  eye.  They  seem  continually 
to  flit  away  from  the  point  of  vision,  and  thus  look  like 
flying  insects.  These  objects  are  present  in  everyone's 
eyes,  and  usually  float  in  the  highest  part  of  the  globe  of 
the  eye,  out  of  the  field  of  vision,  whence  on  any  sudden 
movement  of  the  eye  they  are  dislodged  and  swim  freely 
in  the  vitreous  humour.  They  may  occasionally  pass  in 
front  of  the  central  pit,  and  so  impair  sight.     It  is  a 

'  This  term  is  given  to  the  property  which  certain  substances  possess  of 
becoming  for  a  time  faintly  luminous  as  long  as  they  receive  violet  and 
blue  light.  The  bluish  tint  of  a  solution  of  quinine,  and  the  green  colour 
of  uranium  glass,  depend  on  this  property.  The  fluorescence  of  the  cornea 
and  crystalline  lens  appears  to  depend  upon  the  presence  in  their  tissue  of 
a  very  small  quantity  of  a  substance  like  quinine.  For  the  physiologist 
this  property  is  most  valuable,  for  by  its  aid  he  can  see  the  lens  in  a  living 
eye  by  throwing  on  it  a  concentrated  beam  of  blue  light,  and  thus  ascertain 
that  it  is  placed  close  behind  the  iris,  not  separated  by  a  large  '  posterior 
chamber,'  as  was  long  supposed.  But  for  seeing,  the  fluorescence  of  the 
cornea  and  lens  is  simply  disadvantageous. 

*  Vide  su^rUy  p.  213. 


THE   EYE   AS   AN   OPTICAL   INSTRUMENT.  221 

remarkable  proof  of  the  way  in  which  we  observe,  or  fail 
to  observe,  the  impressions  made  on  our  senses,  that  these 
viuscce  volUantes  often  appear  some-thing  quite  new  and 
disquieting  to  persons  whose  sight  is  beginning  to  suffer 
from  any  cause ;  although,  of  course,  there  must  have  been 
the  same  conditions  long  before. 

A  knowledge  of  the  way  in  which  the  eye  is  developed 
in  man  and  other  vertebrates  explains  these  irregularities 
in  the  structure  of  the  lens  and  the  vitreous  body.  Both 
are  produced  by  an  invagination  of  the  integument  of  the 
embryo.  A  dimple  is  first  formed,  this  deepens  to  a  round 
pit,  and  then  expands  until  its  orifice  becomes  relatively 
minute,  when  it  is  finally  closed  and  the  pit  becomes 
completely  shut  off".  The  cells  of  the  scarf-skin  which 
line  this  hollow  form  the  crystalline  lens,  the  true  skin 
beneath  them  becomes  its  capsule,  and  the  loose  tissue 
which  underlies  the  skin  is  developed  into  the  vitreous 
humour.  The  mark  where  the  neck  of  the  fossa  was  sealed 
is  still  to  be  recognised  as  one  of  the  '  entoptic  images '  of 
many  adult  eyes. 


The  last  defect  of  the  human  eye  which  must  be  noticed 
is  the  existence  of  certain  inequalities  of  the  surface  which 
receives  the  optical  image.  Not  far  from  the  centre  of 
the  field  of  vision  there  is  a  break  in  the  retina,  where 
the  optic  nerve  enters.  Here  there  is  nothing  but  nerve 
fibres  and  blood-vessels  ;  and,  as  the  cones  are  absent,  any 
rays  of  light  which  fall  on  the  optic  nerve  itself  are  un- 
perceived.  This  'blind  spot'  will  therefore  produce  a  corre- 
sponding gap  in  the  field  of  vision  where  nothing  will  be 
visible.  Fig.  32  shows  the  posterior  half  of  the  globe  of  a 
right  eye  which  has  been  cut  across.  E  is  the  retina  with 
its  branching  blood-vessels.  The  point  from  which  these 
diverge  is  that  at  which  the  optic  nerve  enters.  To  the 
reader's  left  is  seen  the  '  yellow  spot.' 


222   RECEXT   PROGRESS   OF   THE   THEORY   OF   VISION. 

Now  the  gap  caused  by  the  presence  of  the  optic  nerve 
is  no  slight  one.  It  is  about  6°  in  horizontal  and  8°  in 
vertical  dimension.  Its  inner  border  is  about  12°  hori- 
zontally distant  from  the  '  temporal '  or  external  side  of 
the  centre  of  distinct  vision.  The  way  to  recognise 
this  blind  spot  most  readily  is  doubtless  known  to  many 
of  my  readers.  Take  a  sheet  of  white  paper  and  mark  on 
it  a  little  cross ;  then  to  the  right  of  this,  on  the  same 
level,  and  about  three  inches  off,  draw  a  round  black  spot 


Fig.  32. 

half  an  inch  in  diameter.  Now,  holding  the  paper  at 
arm's  length,  shut  the  left  eye,  fix  the  right  upon  the 
cross,  and  bring  the  paper  gradually  nearer.  When  it  is 
about  eleven  inches  from  the  eye,  the  black  spot  will 
suddenly  disappear,  and  will  again  come  into  sight  as  the 
paper  is  moved  nearer. 

This  blind  spot  is  so  large  that  it  might  prevent  our 
seeing  eleven  full  moons  if  placed  side  by  side,  or  a  man's 
face  at  a  distance  of  only  six  or  seven  feet.  Mariott^,^  who 
liiscovered  the  phenomenon,  amused  Charles  II.  and  his 

»  Edme.  Mariotte  born  in  Burgundy,  died  at  Paris,  1684, 


THE   EYE   AS   AN   OPTICAL   INSTRUMENT.  .         223 

courtiers  by  showing  them  how  they  might  see  each  other 
with  their  heads  cut  off. 

There  are,  in  addition,  a  number  of  smaller  gaps  in  the 
field  of  vision,  m  which  a  small  bright  point,  a  fixed  star 
for  example,  may  be  lost.  These  are  caused  by  the  blood- 
vessels of  the  retina.  The  vessels  run  in  the  front  layers, 
and  so  cast  their  shadow  on  the  part  of  the  sensative 
mosaic  which  lies  behind  them.  The  larger  ones  shut  off 
the  light  from  reaching  the  rods  and  cones  altogether,  the 
more  slender  at  least  limit  its  amount. 

These  splits  in  the  picture  presented  by  the  eye  may  be 
recoo-nised  by  making  a  hole  in  a  card  with  a  fine  needle, 
and  looking  through  it  at  the  sky,  moving  the  card  a  little 
from  side  to  side  all  the  time.  A  still  better  experiment 
is  to  throw  sunlight  through  a  small  lens  upon  the  white 
of  the  eye  at  the  outer  angle  (temporal  canthus),  while 
the  globe  is  turned  as  much  as  possible  inwards.  The 
shadow  of  the  blood-vessels  is  then  thrown  across  on  to 
the  inner  wall  of  the  retina,  and  we  see  them  as  gigantic 
branching  lines,  like  fig.  32  magnified.  These  vessels  lie 
in  the  front  layer  of  the  retina  itself,  and,  of  course,  their 
shadow  can  only  be  seen  when  it  falls  on  the  proper  sensi- 
tive layer.  So  that  this  phenomenon  furnishes  a  proof 
that  the  hindmost  layer  is  that  which  is  sensitive  to  light. 
And  by  its  help  it  has  become  possible  actually  to  measure 
the  distance  between  the  sensitive  and  the  vascular  layers 
of  the  retina.     It  is  done  as  follows  : — 

If  the  focus  of  the  light  thrown  on  to  the  white  of  the  eye 
(the  sclerotic)  is  moved  slightly  backwards  and  forwards, 
tiie  shadow  of  the  blood-vessels  and  its  image  in  the  field 
of  vision  will,  of  course,  move  also.  The  extent  of  these 
movements  can  be  easily  measured,  and  from  these  data 
Heinrich  Miiller,  of  Wurzburg — whose  too  early  loss  to 
science  we  still  deplore — determined  the  distance  between 
the  two  foci,  and  found  it  exactly  to  equal  the  thickness 


224   RECENT   PROGRESS   OF   THE   THEORY   OF   VISION. 

which  actually  separates  the  layer  of  rods  and  cones  from 
the  vascular  layer  of  the  retina. 

The  condition  of  the  point  of  clearest  vision  (the  yellow 
spot)  is  disadvantageous  in  another  way.  It  is  less  sensi- 
tive to  weak  light  than  the  other  parts  of  the  retina.  It 
has  been  long  known  that  many  stars  of  inferior  magni- 
tude— for  example,  the  Coma  Berenicce  and  the  Pleiades 
— are  seen  more  brightly  if  looked  at  somewhat  obliquely 
than  when  their  rays  fall  full  upon  the  eye.  This  can  be 
proved  to  depend  partly  on  the  yellow  colour  of  the 
macula^  which  weakens  blue  more  than  other  rays.  It  may 
also  be  partly  the  result  of  the  absence  of  vessels  at  this 
yellow  spot  which  has  been  noticed  above,  which  interferes 
with  its  free  communication  with  the  life-giving  blood. 


All  these  imperfections  would  be  exceedingly  trouble 
some  in  an  artificial  camera  obscura  and  in  the  photographic 
picture  it  produced.  But  they  are  not  so  in  the  eye — so 
little,  indeed,  that  it  was  very  difficult  to  discover  some 
of  them.  The  reason  of  their  not  interfering  with  our 
perception  of  external  objects  is  not  simply  that  we  have 
two  eyes,  and  so  one  makes  up  for  the  defects  of  the  other. 
For  even  when  we  do  not  use  both,  and  in  the  case  of 
persons  blind  of  one  eye,  the  impression  we  receive  from 
the  field  of  vision  is  free  from  the  defects  which  the 
irregularity  of  the  retina  would  otherwise  occasion.  The 
chief  reason  is  that  we  are  continually  moving  the  eye, 
and  also  that  the  imperfections  almost  always  affect  those 
parts  of  the  field  to  which  we  are  not  at  the  moment 
directinof  our  attention. 

o 

But,  after  all  it  remains  a  wonderful  paradox,  that 
we  are  so  slow  to  observe  these  and  other  peculiarities 
of  vision  (such  as  the  after-images  of  bright  objects),  so 
long  as  they  are  not  strong  enough  to  prevent  our  seeing 


THE   EYE   AS   AN   OPTICAL   INSTRUMENT.  225 

external  objects.  It  is  a  fact  which  we  constantly  meet, 
not  only  in  optics,  but  in  studying  the  perceptions  pro- 
duced by  other  senses  on  the  consciousness.  The  diffi- 
culty with  which  we  perceive  the  defect  of  the  blind 
spot  is  well  shown  by  the  history  of  its  discovery.  Its 
existence  was  first  demonstrated  by  theoretical  arguments. 
While  the  long  controversy  whether  the  perception  of 
light  resided  in  the  retina  or  the  choroid  was  still  unde- 
cided, Mariotte  asked  himself  what  perception  there  was 
where  the  choroid  is' deficient.  He  made  experiments  to 
ascertain  this  point,  and  in  the  course  of  them  discovered 
the  blind  spot.  Millions  of  men  had  used  their  eyes  for 
ages,  thousands  had  thought  over  the  nature  and  cause 
of  their  functions,  and,  after  all,  it  was  only  by  a  remark- 
able combination  of  circumstances  that  a  simple  pheno- 
menon was  noticed  which  would  apparently  have  revealed 
itself  to  the  slightest  observation.  Even  now,  anyone 
who  tries  for  the  first  time  to  repeat  the  experiment  which 
demonstrates  the  existence  of  the  blind  spot,  finds  it  diffi- 
cult to  divert  his  attention  from  the  fixed  point  of  clear 
vision,  without  losing  sight  of  it  in  the  attempt.  Indeed, 
it  is  only  by  long  practice  in  optical  experiments  that 
even  an  experienced  observer  is  able,  as  soon  as  he  shuts 
one  eye,  to  recognise  the  blank  space  in  the  field  of  vision 
which  corresponds  to  the  blind  spot. 

Other  phenomena  of  this  kind  have  only  been  discovered 
by  accident,  and  usually  by  persons  whose  senses  were 
peculiarly  acute,  and  whose  power  of  observation  was 
unusually  stimulated.  Among  these  may  be  mentioned 
Goethe,  Purkinje,'  and  Johannes  Miiller.^     When  a  sub- 

'  A  distinguished  embryologist,  for  many  years  professor  at  Breslau : 
he  died  at  Prague,  1869,  set.  82. 

2  A  great  biologist,  in  the  full  sense  of  the  term.  He  was  professor  of 
physiology  at  Berlin,  and  died  1858,  set.  57.  His  Manual  of  Physiology 
was  translated  into  English  by  the  late  Dr.  Baly. — Tk. 


226      RECENT   PROGRESS   OF   THE   THEORY   OF   VISION. 

sequent  observer  tries  to  repeat  on  his  own  eyes  these 
experiments  as  he  finds  them  described,  it  is  of  com-se 
easier  for  him  than  for  the  discoverer ;  but  even  now  there 
are  many  of  the  phenomena  described  by  Purkinje  which 
have  never  been  seen  by  anyone  else,  although  it  cannot 
be  certainly  held  that  they  depended  on  individual  pecu- 
liarities of  this  acute  observer's  eyes. 

The  phenomena  of  which  we  have  spoken,  and  a  number 
of  others  also,  may  be  explained  by  the  general  rule  that 
it  is  much  easier  to  recognise  any  change  in  the  condi- 
tion of  a  nerve  than  a  constant  and  equable  impression 
on  it.  In  accordance  with  this  rule,  all  peculiarities  in 
the  excitation  of  separate  nerve  fibres,  which  are  equally 
present  during  the  whole  of  life  (such  as  the  shadow  of 
the  blood-vessels  of  the  eye,  the  yellow  colour  of  the  cen- 
tral pit  of  the  retina,  and  most  of  the  fixed  entoptic 
images),  are  never  noticed  at  all ;  and  if  we  want  to 
observe  them  we  must  employ  unusual  modes  of  illumina- 
tion and,  particularly,  constant  change  of  its  direction. 

According  to  our  present  knowledge  of  the  conditions 
of  nervous  excitation,  it  seems  to  me  to  be  very  unlikely 
that  we  have  here  to  do  with  a  simple  property  of  sensa- 
tion ;  it  must,  I  think,  be  rather  explained  as  a  pheno- 
menon belonging  to  our  power  of  attention,  and  I  now 
only  refer  to  the  question  in  passing,  since  its  full  discus- 
sion will  come  afterwards  in  its  proper  connection. 


So  much  for  the  physical  properties  of  the  Eye.  If  I 
am  asked  why  I  have  spent  so  much  time  in  explaining 
its  imperfection  to  my  readers,  I  answer,  as  I  said  at  first, 
that  I  have  not  done  so  in  order  to  depreciate  the  perfor- 
mances of  this  wonderful  organ  or  to  diminish  our  admi- 
ration of  its  construction.  It  was  my  object  to  make  the 
reader  understand,  at  the  first  step  of  our  inquiry,  that  it 


THE    EYE   AS   AN   OPTICAL   INSTRUMENT.  227 

is  not  any  mechanical  perfection  of  the  organs  of  our 
senses  which  secures  for  us  such  wonderfully  true  and  exact 
impressions  of  the  outer  world.  The  next  section  of  this 
inquiry  will  introduce  much  bolder  and  more  para- 
doxical conclusions  than  any  I  have  yet  stated.  We  have 
now  seen  that  the  eye  in  itself  is  not  by  any  means  so 
complete  an  optical  instrument  as  it  first  appears  :  its 
extraordinary  value  depends  upon  the  way  in  which  we 
use  it :  its  perfection  is  practical,  not  absolute,  consisting 
not  in  the  avoidance  of  every  error,  but  in  the  fact  that 
all  its  defects  do  not  prevent  its  rendering  us  the  most 
important  and  varied  services. 

From  this  point  of  view,  the  study  of  the  eye  gives  us 
a  deep  insight  into  the  true  character  of  organic  adapta- 
tion generally.  And  this  consideration  becomes  still  more 
interesting  when  brought  into  relation  with  the  great  and 
daring  conceptions  which  Darwin  has  introduced  into 
science,  as  to  the  means  by  which  the  progressive  perfec- 
tion of  the  races  of  animals  and  plants  has  been  carried 
on.  Wherever  we  scrutinise  the  construction  of  physio- 
logical organs,  we  find  the  same  character  of  practical 
adaptation  to  the  wants  of  the  organism ;  although,  per- 
haps, there  is  no  instance  which  we  can  follow  out  so 
minutely  as  that  of  the  eye. 

For  the  eye  has  every  possible  defect  that  can  be  found 
in  an  optical  instrument,  and  even  some  which  are  peculiar 
to  itself ;  but  they  are  all  so  counteracted,  that  the  inexact- 
ness of  the  image  which  results  from  their  presence  very 
little  exceeds,  under  ordinary  conditions  of  illumination, 
the  limits  which  are  set  to  the  delicacy  of  sensation  by 
the  dimensions  of  the  retinal  cones.  But  as  soon  as  we 
make  our  observations  under  somewhat  changed  condi- 
tions, we  become  aware  of  the  chromatic  aberration,  t]\e 
astigmatism,  the  blind  spots^  the  yenous  shadows,  the 
11 


228      RECENT   PROGRESS   OF   THE   THEORY   OF   VISION. 

imperfect  transparency  of  the  media,  and  all  the  other 
defects  of  which  I  have  spoken. 

The  adaptation  of  the  eye  to  its  function  is,  therefore, 
most  complete,  and  is  seen  in  the  very  limits  which 
are  set  to  its  defects.  Here  the  result  which  may  be 
reached  by  innumerable  generations  working  under  the 
Darwinian  law  of  inheritance,  coincides  with  what  the 
wisest  Wisdom  may  have  devised  beforehand.  A  sensible 
man  will  not  cut  firewood  with  a  razor,  and  so  w^e  may 
assume  that  each  step  in  the  elaboration  of  the  eye  must 
have  made  the  organ  more  vulnerable  and  more  slow  in 
its  development.  We  must  also  bear  in  mind  that  soft, 
watery  animal  textures  must  always  be  unfavourable  and 
difficult  material  for  an  instrument  of  the  mind. 

One  result  of  this  mode  of  construction  of  the  eye,  of 
which  we  shall  see  the  importance  bye  and  bye,  is  tliat 
clear  and  complete  apprehension  of  external  objects  by 
the  sense  of  sight  is  only  possible  when  we  direct  our 
attention  to  one  part  after  another  of  the  field  of  vision 
in  the  manner  partly  described  above.  Other  conditions, 
which  tend  to  produce  the  same  limitation,  will  after- 
wards come  under  our  notice. 

But,  apparently,  we  are  not  yet  come  much  nearer  to  un- 
derstanding sight.  We  have  only  made  one  step  :  we  have 
learnt  how  the  optical  arrangement  of  the  eye  renders  it 
possible  to  separate  the  rays  of  light  which  come  in  from 
all  parts  of  the  field  of  vision,  and  to  bring  together  again 
all  those  that  have  proceeded  from  a  single  point,  so 
that  they  may  produce  their  effect  upon  a  single  fibre  of 
the  optic  nerve. 

Let  us  see,  therefore,  how  much  we  know  of  the  sensa- 
tions of  the  eye,  and  how  far  this  will  bring  us  towards  the 
solution  of  the  problem. 


II.    The  Sensation  of  Sight. 

In  tlie  first  section  of  our  subject  we  have  followed  the 
course  of  the  rays  of  light  as  far  as  the  retina,  and  seen 
what  is  the  result  produced  by  the  peculiar  arrangement 
of  the  optical  apparatus.  The  light  which  is  reflected 
from  the  separate  illuminated  points  of  external  objects 
is  again  united  in  the  sensitive  terminal  structures  of 
separate  nerve  fibres,  and  thus  throws  them  into  action 
without  affecting  their  neighbours.  At  this  point  the 
older  physiologists  thought  they  had  solved  the  problem, 
so  far  as  it  appeared  to  them  to  be  capable  of  solution. 
External  light  fell  directly  upon  a  sensitive  nervous 
structure  in  the  retina,  and  was,  as  it  seemed,  directly 
felt  there. 

But  during  the  last  century,  and  still  more  during  the 
first  quarter  of  this,  our  knowledge  of  the  processes  which 
take  place  in  the  nervous  system  was  so  far  developed, 
that  Johannes  Miiller,  as  early  as  the  year  1826,^  when 
writing  that  great  work  on  the  '  Comparative  Physiology 
of  Vision,'  which  marks  an  epocli  in  science,  was  able  to 
lay  down  the  most  important  principles  of  the  theory  of 
the  impressions  derived  from  the  senses.  These  prin- 
ciples have  not  only  been  confirmed  in  all  important 
points  by  subsequent  investigation,  but  have  proved  of 
even  more  extensive  application  than  this  eminent  physio- 
logist could  have  suspected. 

The  conclusions  which  he  arrived  at  are  generally  com- 
prehended under  the  name  of  the  theory  of  the  Specific 

'  The  year  In  which  he  was  appointed  Extraordinary  Professor  of  Phy- 
siology in  the  University  of  Bonn. 


230      RECENT   PROGRESS   OF   THE   THEORY   OF   VISION. 

Action  of  the  Senses.  They  are  no  longer  so  novel  that 
they  can  be  reckoned  among  the  latest  advances  of  the 
theory  of  vision,  which  form  the  subject  of  the  present 
essay.  Moreover,  they  have  been  frequently  expounded 
in  a  popular  form  by  others  as  well  as  by  myself.^  But 
that  part  of  the  theory  of  vision  with  which  we  are  now 
occupied  is  little  more  than  a  further  development  of  the 
theory  of  the  specific  action  of  the  senses.  I  must,  there- 
fore, beg  my  reader  to  forgive  me  if,  in  order  to  give  him 
a  comprehensive  view  of  the  whole  subject  in  its  proper 
connection,  I  bring  before  him  much  which  he  already 
knows,  while  I  also  introduce  the  more  recent  additions 
to  our  knowledge  in  their  appropriate  places. 

All  that  we  apprehend  of  the  external  world  is  brought 
to  our  consciousness  by  means  of  certain  changes  which 
are  produced  in  our  organs  of  sense  by  external  impres- 
sions, and  transmitted  to  the  brain  by  the  nerves.  It  is 
in  the  brain  that  these  impressions  first  become  conscious 
sensations,  and  are  combined  so  as  to  produce  our  concep- 
tions of  surrounding  objects.  If  the  nerves  which  convey 
these  impressions  to  the  brain  are  cut  through,  the  sensa- 
tion, and  the  perception  of  the  impression,  immediately 
cease.  In  the  case  of  the  eye,  the  proof  that  visual  per- 
ception is  not  produced  directly  in  each  retina,  but  only 
in  the  brain  itself  by  means  of  the  impressions  transmitted 
to  it  from  both  eyes,  lies  in  the  fact  (which  I  shall  after- 
wards more  fully  explain)  that  the  visual  impression  of 
any  solid  object  of  three  dimensions  is  only  produced  by 
the  combination  of  the  impressions  derived  from  both 
eyes. 

What,  therefore,  we  directly  apprehend  is  not  the  imme- 
diate action  of  the  external  exciting  cause  upon  the  ends 

•  '  On  the  Nature  of  Special  Sensations  in  Man,'  Kbnigsberger  naturwis- 
senschaftliclie  Untcrhaltungen,  vol.  iii.  1852.  '  Human  Vision,'  a  popular 
Scientific  Lecture  by  H.  Helmholtz,  Leipzig,  1855. 


THE   SENSATION   OF   SIGHT.  231 

of  our  nerves,  but  only  the  changed  condition  of  the 
nervous  fibres  which  we  call  the  state  of  excitation  or 
functional  activity. 

Now  all  the  nerves  of  the  body,  so  far  as  we  at  present 
know,  have  the  same  structure,  and  the  change  which  we 
call  excitation  is  in  each  of  them  a  process  of  precisely 
the  same  kind,  whatever  be  the  function  it  subserves.  For 
while  the  task  of  some  nerves  is  that  already  mentioned, 
of  carrying  sensitive  impressions  from  the  external  organs 
to  the  brain,  others  convey  voluntary  impulses  in  the 
opposite  direction,  from  the  brain  to  the  muscles,  caus- 
ing them  to  contract,  and  so  moving  the  limbs.  Other 
nerves,  again,  carry  an  impression  from  the  brain  to 
certain  glands,  and  call  forth  their  secretion,  or  to  the 
heart  and  to  the  blood-vessels,  and  regulate  the  circula- 
tion. But  the  fibres  of  all  these  nerves  are  the  same 
clear,  cylindrical  threads  of  microscopic  minuteness,  con- 
taining the  same  oily  and  albuminous  material.  It  is 
true  that  there  is  a  difference  in  the  diameter  of  the 
fibres,  but  this,  so  far  as  we  know,  depends  only  upon 
minor  causes,  such  as  the  necessity  of  a  certain  strength 
and  of  getting  room  for  a  certain  number  of  independent 
conducting  fibres.  It  appears  to  have  no  relation  to  their 
peculiarities  of  function. 

Moreover,  all  nerves  have  the  same  electro-motor 
actions,  as  the  researches  of  Du  Bois  Reymond  ^  prove. 
In  all  of  them  the  condition  of  excitation  is  called  forth 
by  the  same  mechanical,  electrical,  chemical,  or  thermo- 
metric  changes.  It  is  propagated  with  the  same  rapidity, 
of  about  one  hundred  feet  in  the  second,  to  each  end  of 
the  fibres,  and  produces  the  same  changes  in  their  electro- 
motor properties.  Lastly,  all  nerves  die  when  sub- 
mitted to  like  conditions,  and,  with  a  slight  apparent  dif- 

*  Professor  of  Physiology  in  the  University  of  Berlin. 


232      RECENT   PROGRESS   OF   THE   THEORY   OF   VISION. 

ference  according  to  their  thickness,  undergo  the  same 
coagulation  of  their  contents.  In  short,  all  that  we  can 
ascertain  of  nervous  structure  and  function,  apart  from  the 
action  of  the  other  organs  with  which  they  are  united  and 
in  which  during  life  we  see  the  proofs  of  their  activity,  is 
precisely  the  same  for  all  the  different  kinds  of  nerves. 
Very  lately  the  French  physiologists,  Philippeau  and 
Vulpian,  after  dividing  the  motor  and  sensitive  nerves  of 
the  tongue,  succeeded  in  getting  the  upper  half  of  the 
sensitive  nerve  to  unite  with  the  lower  half  of  the  motor. 
After  the  wound  had  healed,  they  found  that  irritation  of 
the  upper  half,  which  in  normal  conditions  would  have 
been  felt  as  a  sensation,  now  excited  the  motor  branches 
below,  and  thus  caused  the  muscles  of  the  tongue  to 
move.  We  conclude  from  these  facts  that  all  the  differ- 
ence which  is  seen  in  the  excitation  of  different  nerves 
depends  only  upon  the  difference  of  the  organs  to  which 
the  nerve  is  united,  and  to  which  it  transmits  the  state 
of  excitation. 

The  nerve-fibres  have  been  often  compared  with  tele- 
graphic wires  traversing  a  country,  and  the  comparison  is 
well  fitted  to  illustrate  this  striking  and  important  pecu- 
liarity of  their  mode  of  action.  In  the  net-work  of  tele- 
graphs we  find  everywhere  the  same  copper  or  iron  wires 
carrying  the  same  kind  of  movement,  a  stream  of  elec- 
tricity, but  producing  the  most  different  results  in  the 
various  stations  according  to  the  auxiliary  apparatus  with 
which  they  are  connected.  At  one  station  the  effect  is 
the  ringing  of  a  bell,  at  another  a  signal  is  moved,  and  at 
a  third  a  recording  instrument  is  set  to  work.  Chemical 
decompositions  may  be  produced  which  will  serve  to  spell 
out  the  messages,  and  even  the  human  arm  may  be  moved 
by  electricity  so  as  to  convey  telegraphic  signals.  When 
the  Atlantic  cable  was  being  laid.  Sir  William  Thomson 
found  that  the  slightest  signals  could  be  recognised  by  the 


THE   SENSATION   OF   SIGHT.  233 

sense  of  taste,  if  the  wire  was  laid  upon  the  tongue.  Or, 
again,  a  strong  electric  current  may  be  transmitted  by 
telegraphic  wires  in  order  to  ignite  gunpowder  for  blasting 
rocks.  In  short,  everyone  of  the  hundred  different  actions 
which  electricity  is  capable  of  producing  may  be  called 
forth  by  a  telegraphic  wire  laid  to  whatever  spot  we 
please,  and  it  is  always  the  same  process  in  the  wire  itself 
which  leads  to  these  diverse  consequences.  Nerve-fibres 
and  telegraphic  wires  are  equally  striking  examples  to 
illustrate  the  doctrine  that  the  same  causes  may,  under 
different  conditions,  produce  different  results.  However 
commonplace  this  may  now  sound,  mankind  had  to  work 
long  and  hard  before  it  was  understood,  and  before  this 
doctrine  replaced  the  belief  previously  held  in  the  constant 
and  exact  correspondence  between  cause  and  effect.  And 
we  can  scarcely  say  that  the  truth  is  even  yet  universally 
recognised,  since  in  our  present  subject  its  consequences 
have  been  till  lately  disputed. 

Therefore,  as  motor  nerves,  when  irritated,  produce 
movement,  because  they  are  connected  with  muscles, 
and  glandular  nerves  secretion,  because  they  lead  to 
glands,  so  do  sensitive  nerves,  when  they  are  irritated, 
produce  sensation,  because  they  are  connected  with  sensi- 
tive organs.  But  we  have  very  different  kinds  of  sensa- 
tion. In  the  first  place,  the  impressions  derived  from 
external  objects  fall  into  five  groups,  entirely  distinct 
from  each  other.  These  correspond  to  the  five  senses,  and 
their  difference  is  so  great  that  it  is  not  possible  to  com- 
pare in  quality  a  sensation  of  light  with  one  of  sound 
or  of  smell.  We  will  name  this  difference,  so  much 
deeper  than  that  between  comparable  qualities,  a  differ- 
ence of  the  mode,  or  kind,  of  sensation,  and  will  describe 
the  differences  between  impressions  belonging  to  the  same 
sense  (for  example,  the  difference  between  the  various 
sensations  of  colour)  as  a  difference  of  quality. 


234      RECENT   PROGRESS   OF   THE   THEORY   OF   VISION. 

Whether  by  the  irritation  of  a  nerve  we  produce  a 
muscular  movement,  a  secretion  or  a  sensation  depends 
upon  whether  we  are  handling  a  motor,  a  glandular,  or  a 
sensitive  nerve,  and  not  at  all  upon  what  means  of  irrita- 
tion we  may  use.  It  may  be  an  electrical  shock,  or  tearing 
the  nerve,  or  cutting  it  through,  or  moistening  it  with  a 
solution  of  salt,  or  touching  it  with  a  hot  wire.  In  the 
same  way  (and  this  great  step  in  advance  was  due  to 
Johannes  Miiller)  the  kind  of  sensation  which  will  ensue 
when  we  irritate  a  sensitive  nerve,  whether  an  impression 
of  light,  or  of  sound,  or  of  feeling,  or  of  smell,  or  of  taste, 
will  be  produced,  depends  entirely  upon  which  sense  the 
excited  nerve  subserves,  and  not  at  all  upon  the  method 
of  excitation  we  adopt. 

Let  us  now  apply  this  to  the  optic  nerve,  which  is  the 
object  of  our  present  enquiry.  In  the  first  place,  we 
know  that  no  kind  of  action  upon  any  part  of  the  body 
except  the  eye  and  the  nerve  which  belongs  to  it,  can 
ever  produce  the  sensation  of  light.  The  stories  of  som- 
nambulists, which  are  the  only  arguments  that  can  be 
adduced  against  this  belief,  we  may  be  allowed  to  dis- 
believe. But,  on  the  other  hand,  it  is  not  light  alone 
which  can  produce  the  sensation  of  light  upon  the  eye, 
but  also  any  other  power  which  can  excite  the  optic 
nerve.  If  the  weakest  electrical  currents  are  passed 
through  the  eye  they  produce  flashes  of  light.  A  blow, 
or  even  a  slight  pressure  made  upon  the  side  of  the  eye- 
ball with  the  finger,  makes  an  impression  of  light  in  the 
darkest  room,  and,  under  favourable  circumstances,  this 
may  become  intense.  In  these  cases  it  is  important  to 
remember  that  there  is  no  objective  light  produced  in 
the  retina,  as  some  of  the  older  physiologists  assumed, 
for  the  sensation  of  light  may  be  so  strong  that  a  se- 
cond observer  could  not  fail  to  see  through  the  pupil- the 
illumination   of  the  retina  which    would   follow,  if  the 


THE   SENSATION   OF  SIGHT.  235 

sensation  were  really  produced  by  an  actual  development 
of  light  within  the  eye.  But  nothing  of  the  sort  has 
ever  been  seen.  Pressure  or  the  electric  current  excites 
the  optic  nerve,  and  therefore,  according  to  Miiller's 
law,  a  sensation  of  light  results,  but  under  these  cir- 
cumstances, at  least,  there  is  not  the  smallest  spark  of 
actual  light. 

In  the  same  way,  increased  pressure  of  blood,  its  ab- 
normal constitution  in  fevers,  or  its  contamination  with 
intoxicating  or  narcotic  drugs,  can  produce  sensations  of 
light  to  which  no  actual  light  corresponds.  Even  in 
cases  in  which  an  eye  is  entirely  lost  by  accident  or  by 
an  operation,  the  irritation  of  the  stump  of  the  optic 
nerve  while  it  is  healing  is  capable  of  producing  similar 
subjective  effects.  It  follows  from  these  facts  that  the 
peculiarity  in  kind  which  distinguishes  the  sensation  of 
light  from  all  others  does  not  depend  upon  any  peculiar 
qualities  of  light  itself.  Every  action  which  is  capable 
of  exciting  the  optic  nerve  is  capable  of  producing  the 
impression  of  light ;  and  the  purely  subjective  sensation 
thus  produced  is  so  precisely  similar  to  that  caused  by  ex- 
ternal light,  that  persons  unacquainted  with  these  pheno- 
mena readily  suppose  that  the  rays  they  see  are  real  ob- 
jective beams. 

Thus  we  see  that  external  light  produces  no  other 
effects  in  the  optic  nerve  than  other  agents  of  an  entirely 
different  nature.  In  one  respect  only  does  light  differ 
from  the  other  causes  which  are  capable  of  exciting  this 
nerve  :  namely,  that  the  retina,  being  placed  at  the  back 
of  the  firm  globe  of  the  eye,  and  further  protected  by 
the  bony  orbit,  is  almost  entirely  withdrawn  from  other 
exciting  agents,  and  is  thus  only  exceptionally  affected 
by  them,  while  it  is  continually  receiving  the  rays  of 
light  which  stream  in  upon  it  through  the  transparent 
media  of  the  eye. 


236      RECENT  PROGHESS   OF   THE   THEORY  OF  VISION. 

On  the  other  hand,  the  optic  nerve,  by  reason  of  the 
pecuHar  structures  in  connection  with  the  ends  of  its 
fibres,  the  rods  and  cones  of  the  retina,  is  incomparably 
more  sensitive  to  rays  of  light  than  any  other  nervous 
apparatus  of  the  body,  since  the  rest  can  only  be  affected 
by  rays  which  are  concentrated  enough  to  produce  notice- 
able elevation  of  temperature. 

This  explains  why  the  sensations  of  the  optic  nerve  are 
for  us  the  ordinary  sensible  sign  of  the  presence  of  light 
in  the  field  of  vision,  and  why  we  always  connect  the  sen- 
sation of  light  with  light  itself,  even  where  they  are  really 
unconnected.  But  we  must  never  forget  that  a  survey  of 
all  the  facts  in  their  natural  connection  puts  it  beyond 
doubt  that  external  light  is  only  one  of  the  exciting 
causes  capable  of  bringing  the  optic  nerve  into  func- 
tional activity,  and  therefore  that  there  is  no  exclusive 
relation  between  the  sensation  of  light  and  light  itself. 

Now  that  we  have  considered  the  action  of  excitants 
upon  the  optic  nerve  in  general,  we  will  proceed  to  the 
qualitative  differences  of  the  sensation  of  light,  that  is 
to  say,  to  the  various  sensations  of  colour.  We  will  try  to 
ascertain  how  far  these  differences  of  sensation  correspond 
to  actual  differences  in  external  objects. 

Light  is  known  in  Physics  as  a  movement  which  is 
propagated  by  successive  waves  in  the  elastic  ether  distri- 
buted through  the  universe,  a  movement  of  the  same  kind 
as  the  circles  which  spread  upon  the  smooth  surface  of  a 
pond  when  a  stone  falls  on  it,  or  the  vibration  which  is 
transmitted  through  our  atmosphere  as  sound.  The  chief 
difference  is,  that  the  rate  with  which  light  spreads,  and 
the  rapidity  of  movement  of  the  minute  particles  which 
form  the  waves  of  ether,  are  both  enormously  greater  than 
that  of  the  waves  of  water  or  of  air.  The  waves  of  light 
sent  forth  from  the  sun  differ  exceedingly  in  size,  just  as 


THE   SEXSATION   OF   SIGHT.  237 

the  little  ripples  whose  summits  are  a  few  inches  distant 
from  each  other  differ  from  the  waves  of  the  ocean,  be- 
tween whose  foaming  crests  lie  valleys  of  sixty  or  a  him- 
dred  feet.  But,  just  as  high  and  low,  short  and  long  waves, 
on  the  surface  of  water,  do  not  differ  in  kind,  but  only  in 
size,  so  the  various  waves  of  light  which  stream  from  the 
sun  differ  in  their  height  and  length,  but  move  all  in  the 
same  manner,  and  show  (with  certain  differences  depend- 
ing upon  the  length  of  the  waves)  the  same  remark- 
able properties  of  reflection,  refraction,  interference,  dif- 
fraction, and  polarisation.  Hence  we  conclude  that  the 
undulating  movement  of  the  ether  is  in  all  of  them  the 
same.  We  must  particularly  note  that  the  phenomena 
of  interference,  under  which  light  is  now  strengthened, 
and  now  obscured  by  light  of  the  same  kind,  according 
to  the  distance  it  has  traversed,  prove  that  all  the  rays  of 
light  depend  upon  oscillations  of  waves ;  and  further,  that 
the  phenomena  of  polarisation,  which  differ  according  to 
different  lateral  directions  of  the  rays,  show  that  the  par- 
ticles of  ether  vibrate  at  right  angles  to  the  direction  in 
which  the  ray  is  propagated. 

All  the  different  sorts  of  rays  which  I  have  mentioned 
produce  one  effect  in  common.  They  raise  the  tempera- 
ture of  the  objects  on  which  they  fall,  and  accordingly 
are  all  felt  by  our  skin  as  rays  of  heat. 

On  the  other  hand,  the  eye  only  perceives  one  part  of 
these  vibrations  of  ether  as  light.  It  is  not  at  all  cogni- 
sant of  the  waves  of  great  length,  which  I  have  compared 
with  those  of  the  ocean  ;  these,  therefore,  are  named  the 
dark  heat-rays.  Such  are  those  which  proceed  from  a 
warm  but  not  red-hot  stove,  and  which  we  recognise  as 
heat,  but  not  as  light. 

Again,  the  waves  of  shortest  length,  which  correspond 
with  the  very  smallest  ripples  produced  by  a  gentle  breeze, 
are  so  slightly  appreciated  by  the  eye,  that  such  rays  are 


238      RECENT   TROGRESS   OF   THE   THEORY   OF   VISION. 

also  generally  regarded  as  invisible,  and  are  known  as  the 
dark  chemical  rays. 

Between  the  very  long  and  the  very  short  waves  of 
ether  there  are  waves  of  intermediate  length,  which 
strongly  affect  the  eye,  but  do  not  essentially  differ  in 
any  other  physical  property  from  the  dark  rays  of  heat 
and  the  dark  chemical  rays.  The  distinction  between  the 
visible  and  invisible  rays  depends  only  on  the  different 
length  of  their  waves  and  the  different  physical  relations 
which  result  therefrom.  We  call  these  middle  rays  Light, 
because  they  alone  illuminate  our  eyes. 

When  we  consider  the  heating  property  of  these  rays 
we  also  call  them  luminous  heat ;  and  because  they  pro- 
duce such  a  very  different  impression  on  our  skin  and  on 
our  eyes,  heat  was  universally  considered  as  an  entirely 
different  kind  of  radiation  from  light,  until  about  thirty 
years  ago.  But  both  kinds  of  radiation  are  inseparable 
from  one  another  in  the  illuminating  rays  of  the  sun  ; 
indeed,  the  most  careful  recent  investigations  prove  that 
they  are  precisely  identical.  To  whatever  optical  pro- 
cesses they  may  be  subjected,  it  is  impossible  to  weaken 
their  illuminating  power  without  at  the  same  time,  and 
in  the  same  degree,  diminishing  their  heating  and  their 
chemical  action.  Whatever  produces  an  undulatory  move- 
ment of  ether,  of  course  produces  thereby  all  the  effects 
of  the  undulation,  whether  light,  or  heat,  or  fluorescence, 
or  chemical  change. 

Those  undulations  which  strongly  affect  our  eyes,  and 
which  we  call  light,  excite  the  impression  of  different 
colours,  according  to  the  length  of  the  waves.  The  un- 
dulations with  the  longest  waves  appear  to  us  red ;  and 
as  the  length  of  the  waves  gradually  diminishes  they 
seem  to  be  golden-yellow,  yellow,  green,  blue,  violet,  the 
last  colour  being  that  of   the  illuminating  rays  which 


THE   SENSATIOX   OF   SIGHT.  239 

have  the  smallest  wave-length.  This  series  of  colours  is 
universally  known  in  the  rainbow.  We  also  see  it  if  we 
look  towards  the  light  through  a  glass  prism,  and  a  dia- 
mond sparkles  with  hues  which  follow  in  the  same  order. 
In  passing  through  transparent  prisms,  the  primitive 
beam  of  white  light,  which  consists  of  a  multitude  of 
rays  of  various  colour  and  various  wave-length,  is  de- 
composed by  the  different  degree  of  refraction  of  its 
several  parts,  referred  to  in  the  last  essay ;  and  thus 
each  of  its  component  hues  appears  separately.  These 
colours  of  the  several  primary  forms  of  light  are  best 
seen  in  tlie  spectrum  produced  by  a  narrow  streak  of  light 
passing  through  a  glass  prism  :  they  are  at  once  the  fullest 
and  the  most  brilliant  which  the  external  world  can  show. 

Wlien  several  of  these  colours  are  mixed  together,  they 
give  the  impression  of  a  new  colour,  which  generally 
seems  more  or  less  white.  If  they  were  all  mingled  in 
precisely  the  same  proportions  in  which  they  are  com- 
bined in  the  sun-light,  they  would  give  the  impression  of 
perfect  white.  According  as  the  rays  of  greatest,  middle, 
or  least  wave-length  predominate  in  such  a  mixture,  it 
appears  as  reddish-white,  greenish-white,  bluish-white, 
and  so  on. 

Everyone  who  has  watched  a  painter  at  work  knows 
that  two  colours  mixed  together  give  a  new  one.  Now, 
although  the  results  of  the  mixture  of  coloured  light 
differ  in  many  particulars  from  those  of  the  mixture  of 
pigments,  yet  on  the  whole  the  appearance  to  the  eye  is 
similar  in  both  cases.  If  we  allow  two  different  coloured 
lights  to  fall  at  the  same  time  upon  a  white  screen,  or 
upon  the  same  part  of  our  retina,  we  see  only  a  single 
compound  colour,  more  or  less  different  from  the  two 
original  ones. 

The  most  striking  difference  between  the  mixture  of 
pigments   and    that    of    coloured    light    is,    that   while 


240      RECENT   PROGHESS   OF  THE   THEORY   OP  VISION. 

painters  make  green  by  mixing  blue  and  yellow  pig- 
ments, the  union  of  blue  and  yellow  rays  of  light  pro- 
duces white.  The  simplest  way  of  mixing  coloured  light 
is  shown  in  Fig.  33.  P  is  a  small  flat  piece  of  glass  ;  b  and 
g  are  two  coloured  wafers.  The 
observer  looks  at  h  through  the 
glass  plate,  while  g  is  seen  re- 
flected in  the  same ;  and  if  g  is 
put  in  a  proper  position,  its  image 
exactly  coincides  with  that  of  6. 
^  It  then  appears  as  if  there  was 

FlO.  83.  ,  n  1  '   ^  ^ 

a  smgle  wafer  at  6,  with  a  colour 
produced  by  the  mixture  of  the  two  real  ones.  In  this 
experiment  the  light  from  6,  which  traverses  the  glass 
pane,  actually  unites  with  that  from  g,  which  is  reflected 
from  it,  and  the  two  combined  pass  on  to  the  retina  at 
o.  In  general,  then,  light,  which  consists  of  undu- 
lations of  different  wave-lengths,  produces  different  im- 
pressions upon  our  eye,  namely,  those  of  different  colours. 
But  the  number  of  hues  which  we  can  recognise  is 
much  smaller  than  that  of  the  various  possible  com- 
binations of  rays  with  different  wave-lengths  which  ex- 
ternal objects  can  convey  to  our  eyes.  The  retina 
cannot  distinguish  between  the  white  which  is  pro- 
duced by  the  union  of  scarlet  and  bluish-green  light, 
and  that  which  is  composed  of  yellowish-green  and 
violet,  or  of  yellow  and  ultramarine  blue,  or  of  red, 
green,  and  violet,  or  of  all  the  colours  of  the  spectrum 
united.  All  these  combinations  appear  identically  as 
white  ;  and  yet,  from  a  physical  point  of  view,  they  are 
very  different.  In  fact,  the  only  resemblance  between 
the  several  combinations  just  mentioned  is,  that  they  are 
indistinsruishable  to  the  human  eve.  For  instance,  a  sur- 
face  illuminated  with  red  and  bluish-green  light  would 
come  out  black   in  a  photograph  ;  while  another  lighted 


THE  SENSATION  OF  SIGHT.  241 

With  yellowish  green  and  violet  would  appear  very  bright, 
although  both  surfaces  alike  seem  to  the  eye  to  be  simply 
white.  Again,  if  we  successively  illuminate  coloured  ob- 
jects with  white  beams  of  light  of  various  composition, 
they  will  appear  differently  coloured.  And  whenever  we 
decompose  two  such  beams  by  a  prism,  or  look  at  them 
through  a  coloured  glass,  the  difference  between  them  at 
once  becomes  evident. 

Other  colours,  also,  especially  when  they  are  not 
strongly  pronounced,  may,  like  pure  white  light,  be 
composed  of  very  different  mixtures,  and  yet  appear  in- 
distinguishable to  the  eye,  while  in  every  other  property, 
physical  or  chemical,  they  are  entirely  distinct. 

Newton  first  showed  how  to  represent  the  system  of 
colours  distinguishable  to  the  eye  in  a  simple  diagram- 
matic form ;  and  by  the  same  means  it  is  comparatively 
easy  to  demonstrate  the  law  of  the  combination  of  colours. 
The  primary  colours  of  the  spectrum  are  arranged  in  a 
series  around  the  circumference  of  a  circle,  beginning  with 
red,  and  by  imperceptible  degrees  passing  through  the 
various  hues  of  the  rainbow  to  violet.  The  red  and  violet 
are  united  by  shades  of  purple,  which  on  the  one  side  pass 
off  to  the  indigo  and  blue  tints,  and  on  the  other  through 
crimson  and  scarlet  to  orange.  The  middle  of  the  circle 
is  left  white,  and  on  lines  which  run  from  the  centre  to 
the  circumference  are  represented  the  various  tints  which 
can  be  produced  by  diluting  the  full  colours  of  the  cir- 
cumference until  they  pass  into  white.  A  colour-disc  of 
this  kind  shows  all  the  varieties  of  hue  which  can  be 
produced  with  the  same  amount  of  light. 

It  will  now  be  found  possible  so  to  arrange  the  places 
of  the  several  colours  in  tliis  diagram,  and  the  quantity 
of  light  which  each  reflects,  that  when  we  have  ascer- 
tained the  resultants  of  two   coloui-s  of  different  known 


242      RECENT   PROGRESS    OF   THE   THEORY   OF   VISIOIS". 

strength  of  light  (in  the  same  way  as  we  might  determine 
the  centre  of  gravity  of  two  bodies  of  different  known 
weights),  we  shaU  then  find  their  combination-colour 
at  the  '  centre  of  gravity '  of  the  two  amounts  of  light. 


Fig.  34. 


Green 


Blue 


WeUoyt 


\ioUt 


Furplo 


Red 


That  is  to  say,  that  in  a  properly  constructed  colour-disc, 
the  combination-colour  of  any  two  colours  will  be  found 
upon  a  straight  line  drawn  from  between  them ;  and  com- 
pound colours  which  contain  more  of  one  than  of  the 
other  component  hue,  will  be  found  in.  that  proportion 
nearer  to  the  former,  and  further  from  the  latter. 

We  find,  however,  when  we  have  drawn  our  diagram, 
that  those  colours  of  the  spectrum  which  are  most  satu- 
rated in  nature,  and  Avhich  must  therefore  be  placed  at 
the  greatest  distance  from  the  central  white,  will  not 
arrange  themselves  in  the  form  of  a  circle.  The  circum- 
ference of  the  diagram  presents  three  projections  cor- 
responding to  the  red,  the  green,  and  the  violet,  so  that 
the  colour  circle  is  more  properly  a  triangle,  with  the 
corners  rounded  off,  as  seen  in  Fig.  34.  The  continuous 
line  represents  the  curve  of  the  colours  of  the  spectrum, 
and  the  small  circle  in  the  middle  the  white.     At  the  cor- 


THE   SENSATION   OF   SIGHT.  243 

ners  are  the  three  colours  I  have  mentioned,^  and  the  sides 
of  the  triangle  show  the  transitions  from  red  through  yellow 
into  green,  from  green  through  bluish-green  and  ultra- 
marine to  violet,  and  from  violet  through  purple  to  scarlet. 

Newton  used  the  d  iagram  of  the  colours  of  the  spectrum 
(in  a  somewhat  different  form  from  that  just  given) 
only  as  a  convenient  way  of  representing  the  facts  to 
the  eye ;  but  recently  Maxwell  has  succeeded  in  de- 
monstrating the  strict  and  even  quantitative  accuracy 
of  the  principles  involved  in  the  construction  of  this 
diagram.  His  method  is  to  produce  combinations  of 
colours  on  swiftly  rotating  discs,  painted  of  various  tints 
in  sectors.  When  such  a  disc  is  turned  rapidly  round, 
so  that  the  eye  can  no  longer  follow  the  separate  hues, 
they  melt  into  a  uniform  combination-colour,  and  the 
quantity  of  light  which  belongs  to  each  can  be  directly 
measured  by  the  breadth  of  the  sector  of  the  circle  it 
occupies.  Now  the  combination-colours  which  are  pro- 
duced in  this  manner  are  exactly  those  which  would  result 
if  the  same  qualities  of  coloured  light  illuminated  the 
same  surface  continuously,  as  can  be  experimentally 
proved.  Thus  have  the  relations  of  size  and  number 
been  introduced  into  the  apparently  inaccessible  region 
of  colours,  and  their  differences  in  quality  have  been 
reduced  to  relations  of  quantity. 

All  differences  between  colours  may  be  reduced  to  three, 
which  may  be  described  as  difference  of  tone,  difference  of 
fulness,  or,  as  it  is  technically  called,  '  saturation,'  and 
difference  of  brightness.  The  differences  of  tone  are  those 
which  exist  between  the  several  colours  of  the  spectrum, 
and  to  which  we  give  the  names  red,  yellow,  blue,  violet, 
purple.     Thus,  with  regard  to  tone,  colours  form  a  series 

'  The  author  has  restored  violet  as  a  primitive  colour  in  accordance  with 
the  experiments  of  J.  J.  Miiller,  having  in  the  first  edition  adopted  the 
opinion  of  Maxwell  that  it  is  blue. 


244      RECENT   PROGRESS    OF   THE   THEORY   OF   VISIOX. 

which  returns  upon  itself;  a  series  which  we  complete 
when  we  allow  the  terminal  colours  of  the  rainbow  to  pass 
into  one  another  through  purple  and  crimson.  It  is  in 
fact  the  same  which  we  described  as  arranged  around  the 
circumference  of  the  colour-disc. 

The  fulness  or  saturation  of  colours  is  greatest  in  the 
pure  tints  of  the  spectrum,  and  becomes  less  in  proportion 
as  they  are  mixed  with  white  light.  This,  at  least,  is 
true  for  colours  produced  by  external  light,  but  for  our 
sensations  it  is  possible  to  increase  still  further  the 
apparent  saturation  of  colour,  as  we  shall  presently  see. 
Pink  is  a  whitish -crimson,  flesh-colour  a  whitish-scarlet, 
and  so  pale  green,  straw-colour,  light  blue,  &c.,  are  all 
produced  by  diluting  the  corresponding  colours  with 
white.  All  compound  colours  are,  as  a  rule,  less  saturated 
than  the  simple  tints  of  the  spectrum. 

Lastly,  we  have  the  difference  of  brightness,  or  strength 
of  light,  which  is  not  represented  in  the  colour-disc.  As 
long  as  we  observe  coloured  rays  of  light,  difference  in 
brightness  appears  to  be  only  one  of  quantity,  not  of  quality. 
Black  is  only  darkness — that  is,  simple  absence  of  light. 
But  when  we  examine  the  colours  of  external  objects,  black 
corresponds  just  as  much  to  a  peculiarity  of  surface  in 
reflection,  as  does  white,  and  therefore  has  as  good  a  right 
to  be  called  a  colour.  And  as  a  matter  of  fact,  we  find 
in  common  language  a  series  of  terms  to  express  colours 
with  a  small  amount  of  light.  We  call  them  dark  (or 
rather  in  English,  deep)  when  they  have  little  light  but  are 
'  full '  in  tint,  and  grey  when  they  are  '  pale.'  Thus  dark 
blue  conveys  the  idea  of  depth  in  tint,  of  a  full  blue  with 
a  small  amount  of  light ;  while  grey-blue  is  a  pale  blue 
with  a  small  amount  of  light.  In  the  same  way,  the 
colours  known  as  maroon,  bro^vn  and  olive  are  dark, 
more  or  less  saturated  tints  of  red,  yellow  and  green  re- 
spectively. 


THE   SENSATION   OF   SIGHT.  245 

la  this  way  we  may  reduce  all  possible  actual  (ob- 
jective) differences  in  colour,  so  far  as  they  are  appre- 
ciated by  the  eye,  to  three  kinds ;  difference  of  hue  {tone), 
difference  of  fulness  {saturation),  and  difference  of  amount 
of  illumination  {brightness).  It  is  in  this  way  that  we  de- 
scribe the  system  of  colours  in  ordinary  language.  But  we 
are  able  to  express  this  threefold  difference  in  another  way. 

I  said  above  that  a  properly  constructed  colour-disc 
approaches  a  triangle  in  its  outline.  Let  us  suppose  for 
a  moment  that  it  is  an  exact  rectilinear  triangle,  as  made 
by  the  dotted  line  in  Fig.  34  ;  how  far  this  differs  from  the 
actual  condition  we  shall  have  afterwards  to  point  out. 
Let  the  colours  red,  green,  and  violet  be  placed  at  the 
corners,  then  we  see  the  law  which  was  mentioned  above : 
namely,  that  all  the  colours  in  the  interior  and  on  the 
sides  of  the  triangle  are  compounds  of  the  three  at  its 
corners.  It  follows  that  all  differences  of  hue  depend 
upon  combinations  in  different  proportions  of  the  three 
primary  colours.  It  is  best  to  consider  the  three  just 
named  as  primary  ;  the  old  ones  red,  yellow,  and  blue  are 
inconvenient,  and  were  only  chosen  from  experience  of 
painters'  colours.  It  is  impossible  to  make  a  green  out 
of  blue  and  yellow  light. 

We  shall  better  understand  the  remarkable  fact  that  we 
are  able  to  refer  all  the  varieties  in  the  composition  of 
external  light  to  mixtures  of  three  primitive  colours,  if 
in  this  respect  we  compare  the  eye  with  the  ear. 

Sound,  as  I  mentioned  before,  is,  like  light,  an  undulat- 
ing movement,  spreading  by  waves.  In  the  case  of  sound 
also,  we  have  to  distinguish  waves  of  various  length  which 
produce  upon  our  ear  impressions  of  different  quality. 
We  recognise  the  long  waves  as  low  notefs,  the  short 
as  high-pitched,  and  the  ear  may  receive  at  once  many 
waves  of  sound — that  is  to  say,  many  notes.  But  here 
these  do  not  melt  into  compound  notes,  in  the  same  way 


246      RECENT  PROGRESS   OF   THE   THEORY   OF  YlSIOIf, 

that  colours,  when  perceived  at  the  same  time  and  place, 
melt  into  compound  colours.  The  eye  cannot  tell  the 
difference,  if  we  substitute  orange  for  red  and  yellow  ;  but 
if  we  hear  the  notes  C  and  E  sounded  at  the  same  time, 
we  cannot  put  J)  instead  of  them,  without  entirely 
changing  the  impression  upon  the  ear.  The  most  com- 
plicated harmony  of  a  full  orchestra  becomes  changed  to 
our  perception  if  we  alter  any  one  of  its  notes.  No  accord 
(or  consonance  of  several  tones)  is,  at  least  for  the  practised 
ear,  completely  like  another,  composed  of  different  tones  ; 
whereas,  if  the  ear  perceived  musical  tones  as  the  eye 
colours,  every  accord  might  be  completely  represented  by 
combining  only  three  constant  notes,  one  very  low,  one 
very  high,  and  one  intermediate,  simply  changing  the 
relative  strength  of  these  three  primary  notes  to  produce 
all  possible  musical  effects. 

In  reality  we  find  that  an  accord  only  remains  un- 
changed to  the  ear,  when  the  strength  of  each  separate 
tone  which  it  contains  remains  unchanged.  Accordingly,  if 
we  wish  to  describe  it  exactly  and  completely,  the  strength 
of  each  of  its  component  tones  must  be  exactly  stated. 

In  the  same  way,  the  physical  nature  of  a  particular 
kind  of  light  can  only  be  fully  ascertained  by  measuring 
and  noting  the  amount  of  light  of  each  of  the  simple 
colours  which  it  contains.  But  in  sunlight,  in  the  light 
of  most  of  the  stars,  and  in  flames,  we  find  a  continuous 
transition  of  colours  into  one  another  through  numberless 
intermediate  gradations.  Accordingly,  we  must  ascertain 
the  amount  of  light  of  an  infinite  number  of  compound 
rays  if  we  would  arrive  at  an  exact  physical  knowledge  of 
sun  or  starlight.  In  the  sensations  of  the  eye  we  need 
distinguish  for  this  purpose  only  the  varying  intensities 
of  three  components. 

The  practised  musician  is  able  to  catch  the  separate 
notes  of  the  various  instruments  among  the  complicated 


THE   SENSATION   OF   SIGHT.  247 

harmonies  of  an  entire  orchestra,  but  the  optician  cannot 
directly  ascertain  the  composition  of  light  by  means  of 
the  eye  ;  lie  must  make  use  of  the  prism  to  decompose 
the  light  for  him.  As  soon,  however,  as  this  is  done, 
the  composite  character  of  light  becomes  apparent,  and 
he  can  then  distinguish  the  light  of  separate  fixed  stars 
from  one  another  by  the  dark  and  bright  lines  which  the 
spectrum  shows  him,  and  can  recognise  what  chemical 
elements  are  contained  in  flames  which  are  met  with  on 
the  earth,  or  even  in  the  intense  heat  of  the  sun's  at- 
mosphere, in  the  fixed  stars,  or  in  the  nebulae.  The  fact 
that  light  derived  from  each  separate  source  carries  with 
it  certain  permanent  physical  peculiarities  is  the  founda- 
tion of  spectral  analysis — that  most  brilliant  discovery  of 
recent  years,  which  has  opened  the  extreme  limits  of 
celestial  space  to  chemical  analysis. 

There  is  an  extremely  interesting  and  not  very  un- 
common defect  of  sight  which  is  known  as  colour-blind- 
ness. In  this  condition  the  differences  of  colour  are 
reduced  to  a  still  more  simple  system  than  that  described 
above ;  namely,  to  combinations  of  only  two  primary 
colours.  Persons  so  affected  are  called  colour-blind^ 
because  they  confound  certain  hues  which  appear  very 
different  to  ordinary  eyes.  At  the  same  time  they  dis- 
tinguish other  colours,  and  that  quite  as  accurately,  or 
even  (as  it  seems)  rather  more  accurately,  than  ordinary 
people.  They  are  usually  '  red-blind ' ;  that  is  to  say, 
there  is  no  red  in  their  system  of  colours,  and  accordingly 
they  see  no  difference  which  is  produced  by  the  addition 
of  red.  All  tints  are  for  them  varieties  of  blue  and  green 
or,  as  they  call  it,  yellow.  Accordingly  scarlet,  flesh- 
colour,  white,  and  bluish-green  appear  to  them  to  be 
identical,  or  at  the  utmost  to  differ  in  brightness.  The 
same  applies  to  crimson,  violet,  and  blue,  and  to  red, 
orange,  yellow,  and  green.     The  scarlet  flowers  of  the 


248      RECENT   PROGRESS   OF   THE   THEORY   OP   VISION. 

geranium  have  for  them  exactly  the  same  colours  as  its 
leaves.  They  cannot  distinguish  between  the  red  and  the 
green  signals  of  trains.  They  cannot  see  the  red  end 
of  the  spectrum  at  all.  Very  full  scarlet  appears  to  them 
almost  black,  so  that  a  red-blind  Scotch  clergyman  went 
to  buy  scarlet  cloth  for  his  gown,  thinking  it  was  black.* 

In  this  particular  of  discrimination  of  colours,  we  find 
remarkable  inequalities  in  different  parts  of  the  retina. 
In  the  first  place  all  of  us  are  red-blind  in  the  outermost 
part  of  our  field  of  vision.  A  geranium-blossom  when 
moved  backwards  and  forwards  just  within  the  field  of 
sight,  is  only  recognised  as  a  moving  object.  Its  colour 
is  not  seen,  so  that  if  it  is  waved  in  front  of  a  mass 
of  leaves  of  the  same  plant  it  cannot  be  distinguished 
from  them  in  hue.  In  fact,  all  red  colours  appear  much 
darker  when  viewed  indirectly.  This  red-blind  part  of  the 
retina  is  most  extensive  on  the  inner  or  nasal  side  of  the 
field  of  vision ;  and  according  to  recent  researches  of 
Woinow,  there  is  at  the  furthest  limit  of  the  visible  field 
a  narrow  zone  in  which  all  distinction  of  colours  ceases 
and  there  only  remain  differences  of  brightness.  In  this 
outermost  circle  everything  appears  white,  grey,  or  black. 
Probably  those  nervous  fibres  which  convey  impressions 
of  green  light  are  alone  present  in  this  part  of  the  retma. 

In  the  second  place,  as  I  have  already  mentioned,  the 
middle  of  the  retina,  just  around  the  central  pit,  is 
coloured  yellow.  This  makes  all  blue  light  appear  some- 
what darker  in  the  centre  of  the  field  of  sight.  The 
effect  is  particularly  striking  with  mixtures  of  red  and 
greenish-blue,  which  appear  white  when  looked  at  directly, 
but  acquire  a  blue  tint  when  viewed  at  a  slight  distance 

'  A  similar  story  is  told  of  Dalton,  the  author  of  the  'Atomic  Theory.' 
He  was  a  Quaker,  and  went  to  the  Friends'  Meeting,  at  Manchester,  in  a 
pair  of  scarlet  stockings,  which  some  wag  had  put  in  place  of  his  ordinary 
dark  grey  ones. — Tb. 


THE   SENSATION   OF   SIGHT.  249 

from  the  middle  of  the  field  ;  and,  on  the  other  hand, 
wlien  they  appear  white  here,  are  red  to  direct  vision. 
These  inequalities  of  the  retina,  like  the  others  men- 
tioned in  the  former  essay,  are  rectified  by  the  con- 
stant movements  of  the  eye.  We  know  from  the  pale 
and  indistinct  colours  of  the  external  world  as  usually 
seen,  what  impressions  of  indirect  vision  correspond  to 
those  of  direct ;  and  we  thus  learn  to  judge  of  the  colours 
of  objects  according  to  the  impression  which  they  luoiild 
make  on  us  if  seen  directly.  The  result  is,  that  only 
unusual  combinations  and  unusual  or  special  direction  of 
attention  enable  us  to  recognise  the  difference  of  which  I 
have  been  speaking. 

The  theory  of  colours,  with  all  these  marvellous  and 
complicated  relations,  was  a  riddle  which  Goethe  in  vain 
attempted  to  solve  ;  nor  were  we  physicists  and  physio- 
logists more  successful.  I  include  myself  in  the  number ; 
for  I  long  toiled  at  the  task,  without  getting  any 
nearer  my  object,  until  I  at  last  discovered  that  a 
wonderfully  simple  solution  had  been  discovered  at  the 
beginning  of  this  century,  and  had  been  in  print  ever 
since  for  any  one  to  read  who  chose.  This  solution  was 
found  and  published  by  the  same  Thomas  Young  *  who 
first  showed  the  right  method  of  arriving  at  the  in- 
terpretation of  Egyptian  hieroglyphics.  He  was  one 
of  the  most  acute  men  who  ever  lived,  but  had  the 
misfortune  to  be  too  far  in  advance  of  his  contempo- 
raries. They  looked  on  him  with  astonishment,  but  could 
not  follow  his  bold  speculations,  and  thus  a  mass  of  his 
most  important  thoughts  remained  buried  and  forgotten 
in  the  'Transactions  of  the  Eoyal  Society,' until  a  later 
generation  by  slow  degrees  arrived  at  the  rediscovery  of 
his  discoveries,  and  came  to  appreciate  the  force  of  his 
arguments  and  the  accuracy  of  his  conclusions. 

•  Born  at  Milverton,  in  Somersetshire,  1773,  died  1829. 


250      RECEXT   PROGRESS   OF   THE   THEORY   OF   VISION. 

In  proceeding  to  explain  the  theory  of  colours  proposed 
by  him,  I  beg  the  reader  to  notice  that  the  conclusions 
afterwards  to  be  drawn  upon  the  nature  of  the  sensations 
of  sight  are  quite  independent  of  what  is  hypothetical  in 
this  theory. 

Dr.  Young  supposes  that  there  are  in  the  eye  three 
kinds  of  nerve-fibres,  the  first  of  which,  when  irritated  in 
any  way,  produces  the  sensation  of  red,  the  second  the 
sensation  of  green,  and  the  third  that  of  violet.  He 
further  assumes  that  the  first  are  excited  most  strongly 
by  the  waves  of  ether  of  greatest  length ;  the  second, 
which  are  sensitive  tu  green  light,  by  the  waves  of  middle 
length  ;  while  those  which  convey  impressions  of  violet 
are  acted  upon  only  by  the  shortest  vibrations  of  ether. 
Accordingly,  at  the  red  end  of  the  spectrum  the  excita- 
tion of  those  fibres  which  are  sensitive  to  that  colour  pre- 
dominates ;  hence  the  appearance  of  this  part  as  red. 
Further  on  there  is  added  an  impression  upon  the  fibres 
sensitive  to  green  light,  and  thus  results  the  mixed  sensa- 
tion of  yellow.  In  the  middle  of  the  spectrum,  the  nerves 
sensitive  to  green  become  much  more  excited  than  the 
other  two  kinds,  and  accordingly  green  is  the  predominant 
impression.  As  soon  as  this  becomes  mixed  with  violet 
the  result  is  the  colour  known  as  blue  ;  while  at  the  most 
highly  refracted  end  of  the  spectrum  the  impression  pro- 
duced on  the  fibres  which  are  sensitive  to  violet  light 
overcomes  every  other.^ 

It  will  be  seen  that  this  hypothesis  is  nothing  more 
than  a  further  extension  of  Johannes  Miiller's  law  of  special 

*  The  precise  tint  of  the  three  primary  colours  cannot  yet  be  precisely 
ascertained  by  experiment.  The  red  alone,  it  is  certain  from  the  experience 
of  the  colour-blind,  belongs  to  the  extreme  red  of  the  spectrum.  At  the 
other  end  Young  took  violet  for  the  primitive  colour,  while  Maxwell  con- 
siders that  it  is  more  properly  blue.  The  question  is  still  an  open  one: 
acordinq;  to  J.  J.  Miiller's  experiments  {Archivfiir  Ophthalmologic,  XV. 
2.  p.  208)  violet  is  more  probable.  The  fluorescence  of  the  retina  is  here 
a  source  of  difficulty. 


THE   SENSATION   OF   SIGHT.  251 

sensation.  Just  as  the  difference  of  sensation  of  light  and 
warmth  depends  demonstrably  upon  whether  the  rays  of 
the  sun  fall  upon  nerves  of  sight  or  nerves  of  feeling,  so 
it  is  supposed  in  Young's  hypothesis  that  the  difference 
of  sensation  of  colours  depends  simply  upon  whether  one 
or  the  other  kind  of  nervous  fibres  are  more  strongly 
affected.  When  all  three  kinds  are  equally  excited,  the 
result  is  the  sensation  of  white  light. 

The  phenomena  that  occur  in  red-blindness  must  be 
referred  to  a  condition  in  which  the  one  kind  of  nerves, 
which  are  sensitive  to  red  rays,  are  incapable  of  excita- 
tion. It  is  possible  that  this  class  of  fibres  are  wanting, 
or  at  least  very  sparingly  distributed,  along  the  edge  of 
the  retina,  even  in  the  normal  human  e3^e. 

It  must  be  confessed  that  both  in  men  and  in  quadru- 
peds we  have  at  present  no  anatomical  basis  for  this 
theory  of  colours  ;  but  Max  Schultze  has  discovered  a  struc- 
ture in  birds  and  reptiles  which  manifestly  corresponds 
with  what  we  should  expect  to  find.  In  the  eyes  of  many 
of  this  group  of  animals  there  are  found  among  the  rods 
of  the  retina  a  number  which  contain  a  red  drop  of  oil  in 
their  anterior  end,  that  namely  which  is  turned  towards 
the  light ;  while  other  rods  contain  a  yellow  drop,  and 
others  none  at  all.  Now  there  can  be  no  doubt  that  red 
light  will  reach  the  rods  with  a  red  drop  much  better 
than  light  of  any  other  colour,  while  yellow  and  green 
light,  on  the  contrary,  will  find  easiest  entrance  to  the 
rods  with  the  yellow  drop.  Blue  light  would  be  shut  off 
almost  completely  from  both,  but  would  affect  the  colour- 
less rods  all  the  more  effectually.  We  may  therefore  with 
great  probability  regard  these  rods  as  the  terminal  organs 
of  those  nervous  fibres  which  respectively  convey  impres- 
sions of  red,  of  yellow,  and  of  blue  light. 

I  have  myself  subsequently  found  a  similar  hypothesis 
very  convenient   and  well   fitted    to  explain   in  a  most 
12 


252      RECENT   PROGRESS    OF   THE   THEORY   OF   VISION. 

simple  manner  certain  peculiarities  which  have  been 
observed  in  the  perception  of  musical  notes,  peculiarities 
as  enigmatical  as  those  we  have  been  considering  in 
the  eye.  In  the  cochlea  of  the  internal  ear  the  ends 
of  the  nerve  fibres  lie  regularly  spread  out  side  by  side, 
and  provided  with  minute  elastic  appendages  (the  rods 
of  Corti)  arranged  like  the  keys  and  hammers  of  a  piano. 
My  hypothesis  is,  that  here  each  separate  nerve  fibre  is 
constructed  so  as  to  take  cognizance  of  a  definite  note,  to 
which  its  elastic  fibre  vibrates  in  perfect  consonance. 
This  is  not  the  place  to  describe  the  special  characters  of 
our  sensations  of  musical  tones  which  led  me  to  frame 
this  hypothesis.  Its  analogy  with  Young's  theory  of 
colours  is  obvious,  and  it  refers  the  origin  of  overtones, 
the  perception  of  the  quality  of  sounds,  the  difference 
between  consonance  and  dissonance,  the  formation  of  the 
musical  scale  and  other  acoustic  phenomena  to  as  sim- 
ple a  principle  as  that  of  Young.  But  in  the  case 
of  the  ear,  I  could  point  to  a  much  more  distinct 
anatomical  foundation  for  such  a  hypothesis,  and  since 
that  time,  I  have  been  able  actually  to  demonstrate  the 
relation  supposed  ;  not,  it  is  true,  in  man  or  any  verte- 
brate animals,  whose  labyrinth  lies  too  deep  for  experi- 
ment, but  in  some  of  the  marine  Crustacea.  These  animals 
have  external  appendages  to  their  organs  of  hearing 
which  may  be  observed  in  the  living  animal,  jointed  fila- 
ments to  which  the  fibres  of  the  auditory  nerve  are  dis- 
tributed ;  and  Hensen,  of  Kiel,  has  satisfied  himself  that 
some  of  these  filaments  are  set  in  motion  by  certain  notes, 
and  others  by  different  ones. 

It  remains  to  reply  to  an  objection  against  Young's 
theory  of  colour.  I  mentioned  above  that  the  outline  of 
the  coloiu'-disc,  which  marks  the  position  of  the  most 
saturated  colours  (those  of  the  spectrum),  approaches  to  a 
triangle  in  form ;   but  our  conclusions  upon  the  theory  of 


THE   SENSATION   OF   SIGHT.  253 

the  three  primary  colours  depend  upon  a  perfect  rectilinear 
triangle  inclosing  the  complete  colour-system,  for  only  in 
that  case  is  it  possible  to  produce  all  possible  tints  by 
various  combinations  of  the  three  primary  colours  at  the 
angles.  It  must,  however,  be  remembered  that  the 
colour-disc  only  includes  the  entire  series  of  colours 
which  actually  occiu:  in  nature,  while  our  theory  has  to 
do  with  the  analysis  of  our  subjective  sensations  of  colour. 
We  need  then  only  assume  that  actual  coloured  light  does 
not  produce  sensations  of  absolutely  pure  colour ;  that 
red,  for  instance,  even  when  completely  freed  from  all  ad- 
mixture of  white  light,  still  does  not  excite  those  nervous 
fibres  alone  which  are  sensitive  to  impressions  of  red,  but 
also,  to  a  very  slight  degree,  those  which  are  sensitive  to 
green,  and  perhaps  to  a  still  smaller  extent  those  which 
are  sensitive  to  violet  rays.  If  this  be  so,  then  the  sen- 
sation which  the  purest  red  light  produces  in  the  eye  is 
still  not  the  purest  sensation  of  red  which  we  can  con- 
ceive of  as  possible.  This  sensation  could  only  be  called 
forth  by  a  fuller,  pmer,  more  saturated  red  than  has  ever 
been  seen  in  this  world. 

It  is  possible  to  verify  this  conclusion.  We  are  able 
to  produce  artificially  a  sensation  of  the  kind  I  have  de- 
scribed. This  fact  is  not  only  important  as  a  complete 
answer  to  a  possible  objection  to  Young's  theory,  but  is 
also,  as  will  readily  be  seen,  of  the  greatest  importance 
for  understanding  the  real  value  of  our  sensations  of 
colour.  In  order  to  describe  the  experiment  I  must  first 
give  an  account  of  a  new  series  of  phenomena. 

The  result  of  nervous  action  is  fatigue,  and  this  will  be 
proportioned  to  the  activity  of  the  function  performed, 
and  the  time  of  its  continuance.  The  blood,  on  the  other 
hand,  which  flows  in  through  the  arteries,  is  constantly 
performing  its  function,  replacing  used  material  by  fresh, 
and   thus    carrying   away   the   chemical  results    of  func- 


254      RECENT   PROGRESS    OF   THE   THEORY   OF   VISIOX. 

tional  activity;  that  is  to  say,  removing  the  source  of 
fatigue. 

The  process  of  fatigue  as  the  result  of  nervous  action, 
takes  place  in  the  eye  as  well  as  other  organs.  When  the 
entire  retina  becomes  tired,  as  when  we  spend  some  time 
in  the  open  air  in  brilliant  sunshine,  it  becomes  insensible 
to  weaker  light,  so  that  if  we  pass  immediately  into  a 
diml}^  lighted  room  we  see  nothing  at  first ;  we  are  blinded, 
as  we  call  it,  by  the  previous  brightness.  After  a  time 
the  eye  recovers  itself,  and  at  last  we  are  able  to  see,  and 
even  to  read,  by  the  same  dim  light  which  at  first  ap- 
peared complete  darkness. 

It  is  thus  that  fatigue  of  the  entire  retina  shows  itself. 
But  it  is  possible  for  separate  parts  of  that  membrane  to 
become  exhausted,  if  they  alone  have  received  a  strong 
light.  If  we  look  steadily  for  some  time  at  any  bright 
object,  surrounded  by  a  dark  background — it  is  necessary 
to  look  steadily  in  order  that  the  image  may  remain  quiet 
upon  the  retina,  and  thus  fatigue  a  sharply  defined  por- 
tion of  its  surface — and  afterwards  turn  our  eyes  upon  a 
uniform  dark -grey  surface,  we  see  projected  upon  it  an 
after-image  of  the  bright  object  we  were  looking  at  just 
before,  with  the  same  outline  but  with  reversed  illumina- 
tion. What  was  dark  appears  bright,  and  what  was 
bright  dark,  like  the  first  negative  of  a  photographer.  By 
carefully  fixing  the  attention,  it  is  possible  to  produce 
very  elaborate  after-images,  so  much  so  that  occasionally 
even  printing  can  be  distinguished  in  them.  This  phe- 
nomenon is  the  result  of  a  local  fatigue  of  the  retina. 
Those  parts  of  the  membrane  upon  which  the  bright  light 
fell  before,  are  now  less  sensitive  to  the  light  of  the  dark- 
grey  backgroimd  than  the  neighbouring  regions,  and 
there  now  appears  a  dark  spot  upon  the  really  uniform 
surface,  corresponding  in  extent  to  the  surface  of  the 
retina  which  before  received  the  bright  light. 


THE    SENSATION"   OF   SIGHT.  255 

(I  may  here  remark  that  illuminated  sheets  of  white 
paper  are  sufficiently  bright  to  produce  this  after-image. 
If  we  look  at  much  brighter  objects — at  flames,  or  at  the 
sun  itself — the  effect  becomes  complicated.  The  strong 
excitement  of  the  retina  does  not  pass  away  immediately, 
but  produces  a  dii'ect  or  positive  after-image,  which  at 
first  unites  with  the  negative  or  indirect  one  pioduced  by 
the  fatigue  of  the  retina.  Besides  this,  the  effects  of  the 
different  colours  of  white  light  differ  both  in  duration  and 
intensity,  so  that  the  after-images  become  coloured,  and 
the  whole  phenomenon  much  more  complicated.) 

By  means  of  these  after-images  it  is  easy  to  convince 
oneself  that  the  impression  produced  by  a  bright  surface 
begins  to  diminish  after  the  first  second,  and  that  by  the 
end  of  a  single  minute  it  has  lost  from  a  quarter  to  half 
of  its  intensity.  The  simplest  form  of  experiment  for 
this  object  is  as  follows.  Cover  half  of  a  white  sheet  of 
paper  with  a  black  one,  fix  the  eye  upon  some  point  of 
the  white  sheet  near  the  margin  of  the  black,  and  after 
30  to  60  seconds  draw  the  black  sheet  quickly  away, 
without  losing  sight  of  the  point.  The  half  of  the  white 
sheet  which  is  then  exposed  appears  suddenly  of  the  most 
brilliant  brightness  ;  and  thus  it  becomes  apparent  how 
very  much  the  first  impression  produced  by  the  upper  half 
of  the  sheet  had  become  blunted  and  weakened,  even  in 
the  short  time  taken  by  the  experiment.  And  yet,  what 
is  also  important  to  remark,  the  observer  does  not  at  all 
notice  this  fact,  until  the  contrast  brings  it  before  him. 

Lastly,  it  is  possible  to  produce  a  partial  fatigue  of  the 
retina  in  another  way.  We  may  tire  it  for  certain  colours 
only,  by  exposing  either  the  entire  retina,  or  a  portion  of 
it,  for  a  certain  time  (from  half  a  minute  to  five  minutes) 
to  one  and  the  same  colour.  According  to  Young's  theory, 
only  one  or  two  kinds  of  the  optic  nerve  fibres  will  then 
be  fatigued,  those  namely  which  are  sensitive  to  impres- 


256      RECENT   PROGRESS    OF   THE   THEORY   OF   VISION. 

sions  of  the  colour  in  question.  All  the  rest  will  remain 
unaffected.  The  result  is,  that  when  the  after-image 
appears,  red,  we  will  suppose,  upon  a  grey  background, 
the  uniformly  mixed  light  of  the  latter  can  only  produce 
sensations  of  green  and  violet  in  the  part  of  the  retina 
which  has  become  fatigued  by  red  light.  This  part  is 
made  red-blind  for  the  time.  The  after-image  accord- 
ingly appears  of  a  bluish  green,  the  complementary  colour 
to  red. 

It  is  by  this  means  that  we  are  able  to  produce  in 
the  retina  the  pure  and  primitive  sensations  of  satu- 
rated colours.  If,  for  instance,  we  wish  to  see  pure  red, 
we  fatigue  a  part  of  our  retina  by  the  bluish  green  of 
the  spectrum,  which  is  the  complementary  colour  of 
red.  We  thus  make  this  part  at  once  green-blind  and 
violet-blind.  We  then  throw  the  after-image  upon  the 
red  of  as  perfect  a  prismatic  spectrum  as  possible  ;  the 
image  immediately  appears  in  full  and  burning  red,  while 
the  red  light  of  the  spectrum  which  surrounds  it,  although 
the  purest  that  the  world  can  offer,  now  seems  to  the  un- 
fatigued  part  of  the  retina,  less  saturated  than  the  after- 
image, and  looks  as  if  it  were  covered  by  a  whitish  mist. 

These  facts  are  perhaps  enough.  I  will  not  accumu- 
late further  details,  to  understand  which  it  would  be 
necessary  to  enter  upon  lengthy  descriptions  of  many 
separate  experiments. 

We  have  already  seen  enough  to  answer  the  question 
whether  it  is  possible  to  maintain  the  natural  and  innate 
conviction  that  the  quality  of  our  sensations,  and  espe- 
cially our  sensations  of  sight,  give  us  a  true  impression  of 
corresponding  qualities  in  the  outer  world.  It  is  clear 
that  they  do  not.  The  question  was  really  decided  by 
Johannes  Miiller's  deduction  from  well  ascertained  facts 
of  the  la     of  specific  nervous  energy.     Whether  the  rays 


THE   SENSATION   OF   SIGHT.  257 

of  the  sun  appear  to  us  as  colour,  or  as  warmth,  does  not 
at  all  depend  upon  their  own  properties,  but  simply  upon 
whether  they  excite  the  fibres  of  the  optic  nerve,  or  those 
of  the  skin.  Pressure  upon  the  eyeball,  a  feeble  current 
of  electricity  passed  through  it,  a  narcotic  drug  carried  to 
the  retina  by  the  blood,  are  capable  of  exciting  the  sen- 
sation of  light  just  as  well  as  the  sunbeams.  The  most 
complete  difference  offered  by  our  several  sensations,  that 
namely  between  those  of  sight,  of  hearing,  of  taste,  of 
smell,  and  of  touch — this  deepest  of  all  distinctions,  so 
deep  that  it  is  impossible  to  draw  any  comparison  of  like- 
ness, or  unlikeness,  between  the  sensations  of  colour 
and  of  musical  tones — does  not,  as  we  now  see,  at  all  de- 
pend upon  the  nature  of  the  external  object,  but  solely 
upon  the  central  connections  of  the  nerves  which  are 
affected. 

We  now  see  that  the  question  whether  within  the 
special  range  of  each  particular  sense  it  is  possible  to 
discover  a  coincidence  between  its  objects  and  the  sen- 
sations they  produce  is  of  only  subordinate  interest. 
What  colour  the  waves  of  ether  shall  appear  to  us  when 
they  are  perceived  by  the  optic  nerve  depends  upon  their 
length.  The  system  of  naturally  visible  colours  offers  us 
a  series  of  varieties  in  the  composition  of  light,  but  the 
number  of  those  varieties  is  wonderfully  reduced  from  an 
unlimited  number  to  only  three.  Inasmuch  as  the  most 
important  property  of  the  eye  is  its  minute  appreciation 
of  locality,  and  as  it  is  so  much  more  perfectly  organised 
for  this  purpose  than  the  ear,  we  may  be  well  content 
that  it  is  capable  of  recognising  comparatively  few 
differences  in  quality  of  light ;  the  ear,  which  in  the 
latter  respect  is  so  enormously  better  provided,  has  scarcely 
any  power  of  appreciating  differences  of  locality.  But 
it  is  certainly  matter  for  astonishment  to  any  one  who 


258      RECEXT   PROGRESS  OF   THE   THEORY   OF   YISIOX. 

trusts  to  the  direct  information  of  his  natural  senses,  that 
neither  the  limits  within  which  the  spectrum  affects  our 
eyes,  nor  the  differences  of  coloiu:  w^hich  alone  remain 
as  the  simplified  effect  of  all  the  actual  differences  of 
light  in  kind,  should  have  any  other  demonstrable  import 
than  for  the  sense  of  sight.  Light  which  is  piecisely  the 
same  to  our  eyes,  may  in  all  other  physical  and  chemical 
effects  be  completely  different.  Lastly,  we  find  that  the 
unmixed  primitive  elements  of  all  our  sensations  of 
colour  (the  perception  of  the  simple  primary  tints)  can- 
not be  produced  by  any  kind  of  external  light  in  the 
natural  unfatigued  condition  of  the  eye.  These  ele- 
mentary sensations  of  colour  can  only  be  called  forth  by 
artificial  preparation  of  the  organ,  so  that,  in  fact, 
they  only  exist  as  subjective  phenomena.  We  see,  there- 
fore, that  as  to  any  correspondence  in  kind  of  exter- 
nal light  with  the  sensations  it  produces,  there  is  only 
one  bond  of  connection  between  them,  a  bond  which  at 
first  sight  may  seem  slender  enough,  but  is  in  fact  quite 
sufficient  to  lead  to  an  infinite  number  of  most  useful 
applications.  This  law  of  correspondence  between  what 
is  subjective  and  objective  in  vision  is  as  follows: — 

Similar  light  produces  under  like  conditions  a  like 
sensation  of  colour.  Light  which  under  like  conditions 
excites  unlike  sensations  of  colour  is  dissimilar. 

When  two  relations  correspond  to  one  another  in  this 
manner,  the  one  is  a  sign  for  the  other.  Hitherto  the 
notions  of  a  '  sign'  and  of  an  '  image '  or  representation  have 
not  been  carefully  enough  distinguished  in  the  theory  of 
perception  ;  and  this  seems  to  me  to  have  been  the  source 
of  numberless  mistakes  and  false  hypotheses.  In  an 
'  image '  the  representation  must  be  of  the  same  kind  as 
that  which  is  represented.  Indeed,  it  is  only  so  far  an 
image  as  it  is  like  in  kind.  A  statue  is  an  image  of 
a  man,  so  far  as  its  form  reproduces  his :   even  if  it  is 


THE  SENSATION   OF   SIGHT.  259 

executed  on  a  smaller  scalej  every  dimension  will  be 
represented  in  proportion.  A  picture  is  an  image  or 
representation  of  the  original,  first  because  it  represents 
the  colours  of  the  latter  by  similar  colours,  secondly  be- 
cause it  represents  a  part  of  its  relations  in  space— those, 
namely,  which  belong  to  perspective — by  corresponding 
relations  in  space. 

Functional  cerebral  activity  and  the  mental  conceptions 
which  go  with  it  may  be  '  images '  of  actual  occurrences 
in  the  outer  world,  so  far  as  the  former  represent  the 
sequence  in  time  of  the  latter,  so  far  as  they  represent 
likeness  of  objects  by  likeness  of  signs — that  is,  a  regular 
arrangement  by  a  regular  arrangement. 

This  is  obviously  sufficient  to  enable  the  understanding 
to  deduce  what  is  constant  from  the  varied  chanoes  of 
the  external  world,  and  to  formulate  it  as  a  notion  or  a 
law.  That  it  is  also  sufficient  for  all  practical  purposes 
we  shall  see  in  the  next  chapter.  But  not  only  un- 
educated persons,  who  are  accustomed  to  trust  blindly  to 
their  senses,  even  the  educated,  who  know  tliat  their 
senses  may  be  deceived,  are  inclined  to  demur  to  so  com- 
plete a  want  of  any  closer  correspondence  in  kind  between 
actual  objects  and  the  sensations  they  produce  than  the 
law  I  have  just  expounded.  For  instance,  natural  philo- 
sophers long  hesitated  to  admit  the  identity  of  the  rays 
of  light  and  of  heat,  and  exhausted  all  possible  means  of 
escaping  a  conclusion  which  seemed  to  contradict  the 
evidence  of  their  senses. 

Another  example  is  that  of  Groethe,  as  I  have  en- 
deavoured to  show  elsewhere.  He  was  led  to  contradict 
Newton's  theory  of  colours,  because  he  could  not  persuade 
himself  that  white,  which  appears  to  our  sensation  as  the 
purest  manifestation  of  the  brightest  light,  could  be  com- 
posed of  darker  colours.     It  was  Newton's  discovery  of 


200      HECEXT   PROGHESS   OF   THE   THEORY   OP   YISIOJT. 

the  composition  of  light  that  was  the  first  germ  of  the 
modern  doctrine  of  the  true  functions  of  the  senses  ;  and 
in  the  writings  of  his  contemporary,  Locke,  were  correctly 
laid  down  the  most  important  principles  on  which  the 
right  interpretation  of  sensible  qualities  depends.  But, 
however  clearly  we  may  feel  that  here  lies  the  difficulty 
for  a  large  number  of  people,  I  have  never  found  the 
opposite  conviction  of  certainty  derived  from  the  senses 
so  distinctly  expressed  that  it  is  possible  to  lay  hold  of 
the  point  of  error ;  and  the  reason  seems  to  me  to  lie  in 
the  fact  that  beneath  the  popular  notions  on  the  subject 
lie  other  and  more  fundamentally  erroneous  concep- 
tions. 

We  must  not  be  led  astray  by  confounding  the  notions 
of  a  phenomenon  and  an  appearance.  The  colours  of 
objects  are  phenomena  caused  by  certain  real  differences 
in  their  constitution.  They  are.  according  to  the  scientific 
as  well  as  to  the  uninstructed  view,  no  mere  appearance, 
even  though  the  way  in  which  they  appear  depends  chiefly 
upon  the  constitution  of  our  nervous  system.  A  '  decep- 
tive appearance'  is  the  result  of  the  normal  phenomena 
of  one  object  being  confounded  with  those  of  another. 
But  the  sensation  of  colour  is  by  no  means  deceptive 
appearance.  There  is  no  other  way  in  which  colour 
can  appear ;  so  that  there  is  nothing  which  we  could 
describe  as  the  normal  phenomenon,  in  distinction 
from  the  impressions  of  colour  received  through  the 
eye. 

Here  the  principal  difficulty  seems  to  me  to  lie  in  the 
notion  of  quality.  All  difficulty  vanishes  as  soon  as  we 
clearly  understand  that  each  quality  or  property  of  a  thing 
is,  in  reality,  nothing  else  but  its  capability  of  exercising 
certain  effects  upon  other  things.  These  actions  either 
go  on  between  similar  parts  of  the  same  body,  and  so 
produce   the  differences   of  its  aggregate  condition ;    or 


THE    SENSATION   OF   SIGHT.  261 

they  proceed  from  one  body  upon  another,  as  in  the  case 
of  chemical  reactions  ;  or  they  produce  their  effect  on  our 
organs  of  special  sense,  and  are  there  recognised  as  sensa- 
tions, as  those  of  sight,  with  which  we  have  now  to  do. 
Any  of  these  actions  is  called  a  '  property,'  when  its 
object  is  understood  without  being  expressly  mentioned. 
Thus,  when  we  speak  of  the  '  solubility '  of  a  substance, 
we  mean  its  behaviour  toward  water ;  when  we  speak  of 
its  '  weight,'  we  mean  its  attraction  to  the  earth ;  and  in 
the  same  way  we  may  correctly  call  a  substance  '  blue,' 
understanding,  as  a  tacit  assumption,  that  we  are  only 
speaking  of  its  action  upon  a  normal  eye. 

But  if  what  we  call  a  property  always  implies  an  action 
of  one  thing  on  another,  then  a  property  or  quality  can 
never  depend  upon  the  nature  of  one  agent  alone,  but 
exists  only  in  relation  to,  and  dependent  on,  the  nature 
of  some  second  object,  which  is  acted  upon.  Hence, 
there  is  really  no  meaning  in  talking  of  properties  of 
light  which  belong  to  it  absolutely,  independent  of  all 
other  objects,  and  which  we  may  expect  to  find  repre- 
sented in  the  sensations  of  the  human  eye.  The  notion 
of  such  properties  is  a  contradiction  in  itself.  They 
cannot  possibly  exist,  and  therefore  we  cannot  expect  to 
find  any  coincidence  of  our  sensations  of  colour  with 
qualities  of  light. 

These  considerations  have  naturally  long  ago  sug- 
gested themselves  to  thoughtful  minds ;  they  may  be 
found  clearly  expressed  in  the  writings  of  Locke  and 
Herbart,'  and  they  are  completely  in  accordance  with 
Kant's  philosophy.  But  in  former  times,  they  demanded 
a  more  than  usual  power  of  abstraction,  in  order  that 
their  truth  should  be  understood ;  whereas  now  the  facts 

'  Johann  Friedrich  Herbart,  born  1776,  died  1841,  professor  of  philo- 
sophy at  Konigsberg  and  Gottingen.  author  of  Psychologie  ah  Wissew 
schaft,  neugegrundet  auf  Erfahrung,  Metaphysik  und  Mathematik. — Te. 


262      RECENT   PROGRESS    OF   THE   THEORY   OF   TISION. 

which  we  have  laid  before  the  reader  illustrate  them  in 
the  clearest  manner. 

After  this  excursion  into  the  world  of  abstract  ideas, 
we  return  once  more  to  the  subject  of  colour,  and  will 
now  examine  it  as  a  sensible  '  sign '  of  certain  external 
qualities,  either  of  light  itself  or  of  the  objects  which 
reflect  it. 

It  is  essential  for  a  good  sign  to  be  constant — that  is, 
the  same  sign  must  always  denote  the  same  object.  Now, 
we  have  already  seen  that  in  this  particular  our  sensations 
of  colour  are  imperfect ;  they  are  not  quite  uniform  over 
the  entire  field  of  the  retina.  But  the  constant  move- 
ment of  the  eye  supplies  this  imperfection,  in  the  same 
way  as  it  makes  up  for  the  unequal  sensitiveness  of  the 
different  parts  of  the  retina  to  form. 

We  have  also  seen  that  when  the  retina  becomes  tired, 
the  intensity  of  the  impression  produced  on  it  rapidly 
diminishes,  but  here  again  the  usual  effect  of  the  constant 
movements  of  the  eye  is  to  equalise  the  fatigue  of  the 
various  parts,  and  hence  we  rarely  see  after-images.  If 
they  appear  at  all,  it  is  in  the  case  of  brilliant  objects  like 
very  bright  flames,  or  the  sun  itself.  And,  so  long  as  the 
fatigue  of  the  entire  retina  is  uniform,  the  relative 
brightness  and  colour  of  the  different  objects  in  sight 
remains  almost  unchanged,  so  that  the  effect  of  fatigue 
is  gradually  to  weaken  the  apparent  illumination  of  the 
entire  field  of  vision. 

This  brings  us  to  consider  the  differences  in  the  pictures 
presented  by  the  eye,  which  depend  on  different  degrees 
of  illumination.  Here  again  we  meet  with  instructive 
facts.  We  look  at  external  objects  under  light  of  very 
different  intensity,  varying  from  the  most  dazzling  sun- 
shine to  the  pale  beams  of  the  moon  ;  and  the  light  of 
the  full  moon  is  1 50,000  times  less  than  that  of  the  sun. 


THE   SENSATION   OF   SIGHT.  263 

Moreover,  the  colour  of  the  ilhimination  may  vary 
greatly.  Thus,  we  sometimes  employ  artificial  light,  and 
this  is  always  more  or  less  orange  in  colour ;  or  the 
natural  daylight  is  altered,  as  we  see  it  in  the  green  shade 
of  an  arbour,  or  in  a  room  with  coloured  carpets  and 
curtains.  As  the  brightness  and  the  colour  of  the  illu- 
mination changes,  so  of  course  will  the  brightness  and 
colour  of  the  light  which  the  illuminated  objects  reflect 
to  our  eyes,  since  all  differences  in  local  colour  depend 
upon  different  bodies  reflecting  and  absorbing  various 
proportions  of  the  several  rays  of  the  sun.  Cinnabar 
reflects  the  rays  of  great  wave  length  without  any  obvious 
loss,  while  it  absorbs  almost  the  whole  of  the  other  rays. 
Accordingly,  this  substance  appears  of  the  same  red  colour 
as  the  beams  which  it  throws  back  into  the  eye.  If  it  is 
illuminated  with  light  of  some  other  colour,  without  any 
mixture  of  red,  it  appears  almost  black. 

These  observations  teach  what  we  find  confirmed  by 
daily  experience  in  a  hundred  ways,  that  the  apparent 
colour  and  brightness  of  illuminated  objects  varies  with 
the  colour  and  brightness  of  the  illumination.  This  is  a 
fact  of  the  first  importance  for  the  painter,  for  many  of 
his  finest  efifects  depend  on  it. 

But  what  is  most  important  practically  is  for  us  to  be 
able  to  recognise  surrounding  objects  when  we  see  them : 
it  is  only  seldom  that,  for  some  artistic  or  scientific  pur- 
pose, we  turn  our  attention  to  the  way  in  which  they  are 
illuminated.  Now  what  is  constant  in  the  colour  of  an 
object  is  not  the  brightness  and  colour  of  the  light  which 
it  reflects,  but  the  relation  between  the  intensity  of  the 
different  coloured  constituents  of  this  light,  on  the  one 
hand,  and  that  of  the  corresponding  constituents  of  the 
light  which  illuminates  it  on  the  other.  This  proportion 
alone  is  the  expression  of  a  constant  property  of  the 
object  in  question. 


264      JRECEXT   PEOGRESS   OF   THE   THEORY   OF  VISION. 

Considered  theoretically,  the  task  of  judging  of  the 
colour  of  a  body  under  changing  illumination  would  seem 
to  be  impossible  ;  but  in  practice  we  soon  find  that  we 
are  able  to  judge  of  local  colour  without  the  least  un- 
certainty or  hesitation,  and  under  the  most  different 
conditions.  For  instance,  white  paper  in  full  moonlight 
is  darker  than  black  satin  in  daylight,  but  we  never  find 
any  difficulty  in  recognising  the  paper  as  white  and  the 
satin  as  black.  Indeed,  it  is  much  more  difficult  to 
satisfy  ourselves  that  a  dark  object  with  the  sun  shining 
on  it  reflects  light  of  exactly  the  same  colour,  and 
perhaps  the  same  brightness,  as  a  white  object  in  sha- 
dow, than  that  the  proper  colour  of  a  white  paper  in 
shadow  is  the  same  as  that  of  a  sl.eet  of  the  same  kind 
lying  close  to  it  in  the  sunlight.  Grey  seems  to  us 
something  altogether  different  from  white,  and  so  it  is, 
regarded  as  a  proper  colour ; »  for  anything  which  only 
reflects  half  the  light  it  receives  must  have  a  different 
surface  from  one  which  reflects  it  all.  And  yet  the  im- 
pression upon  the  retina  of  a  grey  surface  under  illumi- 
nation may  be  absolutely  identical  with  that  of  a  white 
surface  in  the  shade.  Every  painter  represents  a  white 
object  in  shadow  by  means  of  grey  pigment,  and  if  he 
has  correctly  imitated  nature,  it  appears  pure  white.  In 
order  to  convince  one's  self  of  the  identity  in  this  respect 
— i.e.  as  illumination  colours — of  grey  and  white,  the 
following  experiment  may  be  tried.  Cut  out  a  circle  in 
grey  paper,  and  concentrate  a  strong  beam  of  light  upon 
it  with  a  lens,  so  that  the  limits  of  the  illumination 
exactly  correspond  with  those  of  the  grey  circle.     It  will 

'  The  local  or  proper  colour  of  an  object  (Kbrperfarhe)  is  that  which  it 
shows  in  common  white  light,  while  the  'illumination  colour,'  as  I  have 
translated  Lichtfarbe,  is  that  which  is  produced  by  coloured  light.  Thus 
the  red  of  some  sandstone  rocks  seen  by  common  white  light  is  their  proper 
colour,  that  of  a  snow  mountain  in  the  rays  of  the  setting  sun  is  an  illu- 
mination-colour.— Tb. 


THE  SENSATION   OF   SIGHT.  265 

then  be  impossible  to  tell  that  there  is  any  artificial  il- 
lumination at  all.     The  grey  looks  white.' 

We  may  assume,  and  the  assumption  is  justified  by 
certain  phenomena  of  contrast,  that  illumination  of  the 
brightest  white  we  can  produce,  gives  a  true  criterion  for 
judging  of  the  darker  objects  in  the  neighbourhood,  since, 
under  ordinary  circumstances,  the  brightness  of  any  proper 
colour  diminishes  in  proportion  as  the  illumination  is 
diminished,  or  the  fatigue  of  the  retina  increased. 

This  relation  holds  even  for  extreme  degrees  of  illu- 
mination, so  far  as  the  objective  intensity  of  the  light  is 
concerned,  but  not  for  our  sensation.  Under  illumination 
so  brilliant  as  to  approach  what  would  be  blinding,  degrees 
of  brightness  of  light-coloured  objects  become  less  and 
less  distinguishable  ;  and,  in  the  same  way,  when  the 
illumination  is  very  feeble,  we  are  unable  to  appreciate 
slight  differences  in  the  amount  of  light  reflected  by  dark 
objects.  The  result  is  that  in  sunshine  local  colours  of 
moderate  brightness  approach  the  brightest,  whereas  in 
moonlight  they  approach  the  darkest.  The  painter  utilises 
this  difference  in  order  to  represent  noonday  or  midnight 
scenes,  although  pictures,  which  are  usually  seen  in  uni- 
form daylight,  do  not  really  admit  of  any  difference  of 
brightness  approaching  that  between  sunshine  and  moon- 
light. To  represent  the  former,  he  paints  the  objects  of 
moderate  brightness  almost  as  bright  as  the  brightest ;  for 
the  latter,  he  makes  them  almost  as  dark  as  the  darkest. 

The  effect  is  assisted  by  another  difference  in  the  sen- 
sation produced  by  the  same  actual  conditions  of  light  and 
colour.  If  the  brightness  of  various  colours  is  equally  in- 
creased, that  of  red  and  yellow  becomes  apparently  stronger 
than  that  of  blue.  Thus,  if  we  select  a  red  and  a  blue  paper 
which  appear  of  the  same  brightness  in  ordinary  daylight, 

'  The  demonstration  is  more  striking  if  the  grey  disk  is  placed  on  a  sheet 
of  white  paper  in  diffused  light. — Te. 


2QQ      RECENT   PROGRESS   OF   THE   THEORY   OF  VISION. 

the  red  seems  much  brighter  in  full  sunlight,  the  blue  in 
moonlight  or  starlight.  This  peculiarity  in  our  perception 
is  also  made  use  of  by  painters  ;  they  make  yellow  tints 
predominate  when  representing  landscapes  in  full  sun- 
sliine,  while  every  object  of  a  moonlight  scene  is  given  a 
shade  of  blue.  But  it  is  not  only  local  colour  which  is 
thus  affected  ;  the  same  is  true  of  the  colours  of  the 
spectrum. 

These  examples  show  very  plainly  how  independent  our 
judgment  of  colours  is  of  their  actual  amount  of  illu- 
mination. In  the  same  way,  it  is  scarcely  affected  by  the 
colour  of  the  illumination  We  know,  of  course,  in  a 
general  way  that  candle-light  is  yellowish  compared  with 
daylight,  but  we  only  learn  to  appreciate  how  much  the 
two  kinds  of  illumination  differ  in  colour  when  we  bring 
them  together  of  the  same  intensity — as,  for  example,  in 
the  experiment  of  coloured  shadotus.  If  we  admit  light 
from  a  cloudy  sky  through  a  narrow  opening  into  a  dark 
room,  so  that  it  falls  sidesvays  on  a  horizontal  sheet  of 
white  paper,  while  candle-light  falls  on  it  from  the  other 
side,  and  if  we  then  hold  a  pencil  vertically  upon  the 
paper,  it  will  of  course  throw  two  shadows  :  the  one  made 
by  the  daylight  will  be  orange,  and  looks  so ;  the  other 
made  by  the  candle-light  is  really  white,  but  appears  blue 
by  contrast.  The  blue  and  the  orange  of  the  two  shadows 
are  both  colours  which  we  call  white,  when  we  see  them 
by  daylight  and  candle-light  respectively.  Seen  to- 
gether, they  appear  as  two  very  different  and  tolerably 
saturated  colours,  yet  we  do  not  hesitate  a  moment  in 
recognising  white  paper  by  candle-light  as  white,  and 
very  different  from  orange.* 

The  most  remarkable  of  this  series  of  facts  is  that  we 
can  separate  the  colour  of  any  transparent  medium  from 

'  This  experiment  with  diffused  white  day-light  may  also  be  made  with 
moonlight. 


THE   SEI^SATIOI!^   OF   SIGHT.  267 

that  of  objects  seen  through  it.  This  is  proved  by  a 
number  of  experiments  contrived  to  illustrate  the  effects 
of  contrast.  If  we  look  through  a  green  veil  at  a  field  of 
snow,  although  the  light  reflected  from  it  must  really 
have  a  greenish  tint  when  it  reaches  our  eyes,  yet  it 
appears,  on  the  contrary,  of  a  reddish  tint,  from  the  effect 
of  the  indirect  aftei-image  of  green.  So  completely 
are  we  able  to  separate  the  light  which  belongs  to  the 
transparent  medium  from  that  of  the  objects  seen 
through  it.' 

The  changes  of  colour  in  the  two  last  experiments  are 
known  as  phenomena  of  contrast.  They  consist  in  mis- 
takes as  to  local  colour,  which  for  the  most  part  depend 
upon  imperfectly  defined  after-images.^  This  effect  is 
known  as  successive  contrast,  and  is  experienced  when  the 
eye  passes  over  a  series  of  coloured  objects.  But  a  similar 
mistake  may  result  from  our  custom  of  judging  of  local 
colour  according  to  the  brightness  and  colour  of  the 
various  objects  seen  at  the  same  time.  If  these  relations 
happen  to  be  different  from  what  is  usual,  contrast  phe- 
nomena ensue.  When,  for  example,  objects  are  seen 
under  two  different  coloured  illuminations,  or  through 
two  different  coloured  media  (whether  real  or  apparent), 
these  conditions  produce  what  is  called  shnultaneous 
contrast.  Thus  in  the  experiment  described  above  of 
coloured  shadows  thrown  by  daylight  and  candle-light, 
the  doubly  illuminated  surface  of  the  paper  being  tlie 
brightest  object  seen,  gives  a  false  criterion  for  white.  Com- 
pared with  it,  the  really  white  but  less  bright  light  of  the 
shadow  thrown  by  the  candle  looks  blue.  Moreover,  in 
these  curious  effects  of  contrast,  we  must  take  into  account 

*  A  number  of  similar  experiments  will  be  found  described  in  the 
author's  Handbuch  der  fhysiologischen  Optik,  pp.  398-411. 

2  These  after-images  have  been  described  as  '  accidental  images,'  positive 
when  of  the  same  colour  as  the  original  colour,  negative  when  of  the  com- 
plementary colour. — Tb. 


268      BKCENT   PROGRESS    OF   THE   THEORY   OF   VISION. 

that  differences  in  sensation  which  are  easily  appre- 
hended appear  to  us  greater  than  those  less  obvious. 
Differences  of  colour  which  are  actually  before  our  eyes 
are  more  easily  apprehended  than  those  which  we  only 
keep  in  memory,  and  contrasts  between  objects  which  are 
close  to  one  another  in  the  field  of  vision  are  more  easily 
recognised  than  when  they  are  at  a  distance.  All  this 
contributes  to  the  effect.  Indeed,  there  are  a  number  of 
subordinate  circumstances  affecting  the  result  which  it 
would  be  very  interesting  to  follow  out  in  detail,  for  they 
throw  great  light  upon  the  way  in  which  we  judge  of 
local  colour :  but  we  must  not  pursue  the  inquiry  further 
here.  I  will  only  remark  that  all  these  effects  of  contrast 
are  not  less  interesting  for  the  scientific  painter  than  for 
the  physiologist,  since  he  must  often  exaggerate  the 
natural  phenomena  of  contrast,  in  order  to  produce  the 
impression  of  greater  varieties  of  light  and  greater  fulness 
of  colour  than  can  be  actually  produced  by  artificial 
pigments. 

Here  we  must  leave  the  theory  of  the  Sensations  of 
Sight.  This  part  of  our  inqiiiry  has  shown  us  that  tl>e 
qualities  of  these  sensations  can  only  be  regarded  as  signs 
of  certain  different  qualities,  which  belong  sometimes  to 
light  itself,  sometimes  to  the  bodies  it  illuminates,  but 
that  there  is  not  a  single  actual  quality  of  the  objects 
seen  which  precisely  corresponds  to  our  sensations  of  sight. 
Nay,  we  have  seen  that,  even  regarded  as  signs  of  real 
phenomena  in  the  outer  world,  they  do  not  possess  the 
one  essential  requisite  of  a  complete  system  of  signs — 
namely,  constancy — with  anything  like  completeness  ;  so 
that  all  that  we  can  say  of  our  sensations  of  sight  is, 
that  '  under  similar  conditions,  the  qualities  of  this  sen- 
sation appear  in  the  same  way  for  the  same  objects.' 

And  yet,  in  spite  of  all  this  imperfection,  we  have  also 


THE   SENSATION   OF   SIGHT.  269 

found  that  by  means  of  so  inconstant  a  system  of  signs, 
we  are  able  to  accomplish  the  most  important  part  of  our 
task — to  recognise  the  same  proper  colours  wherever  they 
occur  ;  and,  considering  the  difficulties  in  the  way,  it  is 
surprising  how  well  we  succeed.  Out  of  this  inconstant 
system  of  brightness  and  of  colours,  varying  according  to 
the  illumination,  varying  according  to  the  fatigue  of  the 
retina,  varying  according  to  the  part  of  it  affected,  we  are 
able  to  determine  the  proper  colour  of  any  object,  the  one 
constant  phenomenon  which  corresponds  to  a  constant 
quality  of  its  surface ;  and  this  we  can  do,  not  after  long 
consideration,  but  by  an  instantaneous  and  involuntary 
decision. 

The  inaccuracies  and  imperfections  of  the  eye  as  an 
optical  instrument,  and  those  which  belong  to  the  image 
on  the  retina,  now  appear  insignificant  in  comparison  with 
the  incongruities  which  we  have  met  with  in  the  field  of 
sensation.  One  might  almost  believe  that  Nature  had 
here  contradicted  herself  on  purpose,  in  order  to  destroy 
any  dream  of  a  pre-existing  harmony  between  the  outer 
and  the  inner  world. 

And  what  progress  have  we  made  in  our  task  of  ex- 
plaining Sight  ?  It  might  seem  that  we  are  farther  off 
than  ever  ;  the  riddle  only  more  complicated,  and  less 
hope  than  ever  of  finding  out  the  answer.  The  reader 
may  perhaps  feel  inclined  to  reproach  Science  with  only 
knowing  how  to  break  up  with  fruitless  criticism  the  fair 
world  presented  to  us  by  our  senses,  in  order  to  annihi- 
late the  fragments. 

Woe !  woe  ! 

Thou  hast  destroyed 

The  beautiful  world 

With  powerful  fist ; 

In  ruin  'tis  hurled, 

By  the  blow  of  a  demigod  shattered. 


270  THE   PEECEPTION   OF   SIGHT. 

The  scattered 

Fragments  into  the  void  we  carry, 

DeyJoring 

The  beauty  perished  beyond  restoring.* 

and  may  feel  determined  to  stick  fast  to  the  '  sound  com- 
mon sense '  of  mankind,  and  believe  his  own  senses  more 
than  physiology. 

But  there  is  still  a  part  of  our  investigation  which  we 
have  not  touched — that  into  our  conceptions  of  space. 
Let  us  see  whether,  after  all,  our  natural  reliance  upon  tlie 
accuracy  of  what  our  senses  teach  us,  will  not  be  justified 
even  before  the  tribunal  of  Science. 


III.     The  Pehception  of  Sight. 

The  colours  which  have  been  the  subject  of  the  last 
chapter  are  not  only  an  ornament  we  sliould  be  sorry  to 
lose,  but  are  also  a  means  of  assisting  us  in  the  distinction 
and  recognition  of  external  objects.  But  the  importance 
of  colour  for  this  purpose  is  far  less  than  the  means  which 
the  rapid  and  far-reaching  power  of  the  eye  gives  us  of 
distinguishing  the  various  relations  of  locality,  No  other 
sense  can  be  compared  with  the  eye  in  this  respect.  The 
sense  of  touch,  it  is  true,  can  distinguish  relations  of 
space,  and  has  the  special  power  of  judging  of  all  matter 

*  Bayard  Taylor's  translation  of  the  passage  in  Faust : — 

Du  hast  sie  zerstort 

Die  schone  Welt 

Mit  machtiger  Faust ; 

Sie  stiirzt,  sie  zerfallt, 

Ein  Halbgott  hat  sie  zerschlagen. 

Wir  tragen 

Die  Triimmern  ins  Nichts  hiniiber, 

Und  klagen 

Ueber  die  verlorne  Schone. 


THE   PERCEPTION   OF  SIGHT.  271 

within  reach,  at  once  as  to  resistance,  volume,  and  weight; 
but  the  range  of  touch  is  Hmited,  and  the  distinction  it 
can  make  between  small  distances  is  not  nearly  so  accu- 
rate as  that  of  sight.  Yet  the  sense  of  touch  is  sufficient, 
as  experiments  upon  persons  born  blind  have  proved,  to 
develop  complete  notions  of  space.  This  proves  that  the 
possession  of  sight  is  not  necessary  for  the  formation  of 
these  conceptions,  and  we  shall  soon  see  that  we  are  con- 
tinually controlling  and  correcting  the  notions  of  locality 
derived  from  the  eye  by  the  help  of  the  sense  of  touch, 
and  always  accept  the  impressions  on  the  latter  sense  as 
decisive.  The  two  senses,  which  really  have  the  same 
task,  though  with  very  different  means  of  accomplishing 
it,  happily  supply  each  other's  deficiencies.  Touch  is  a 
trustworthy  and  experienced  servant,  but  enjoys  only  a 
limited  range,  while  sight  rivals  the  boldest  flights  of 
fancy  in  penetrating  to  illimitable  distances. 

This  combination  of  the  two  senses  is  of  great  im- 
portance for  our  present  task ;  for,  since  we  have  heie 
only  to  do  with  vision,  and  since  touch  is  sufficient  to 
produce  complete  conceptions  of  locality,  we  may  assume 
these  conceptions  to  be  already  complete,  at  least  in  their 
general  outline,  and  may,  accordingly,  confine  our  in- 
vestigation to  ascertaining  the  common  point  of  agree- 
ment between  the  visual  and  tactile  perceptions  of  space. 
The  question  how  it  is  possible  for  any  conception  of 
locality  to  arise  from  either  or  both  of  these  sensations, 
we  will  leave  till  last. 

It  is  obvious,  from  a  consideration  of  well-known  facts, 
that  the  distribution  of  our  sensations  among  nervous 
structures  separated  from  one  another  does  not  at  all 
necessarily  bring  with  it  the  conception  that  the  causes  of 
these  sensations  are  locally  separate.  For  example,  we 
may  have  sensations  of  light,  of  warmth,  of  various  notes 
of  music,  and  also  perhaps  of  an  odour,  in  the  same  room, 


272      RECENT   PROGHESS   OF   THE   THEORY   OF   VISION. 

and  may  recognise  that  all  these  agents  are  diffused 
throuo'h  the  air  of  the  room  at  the  same  time,  and  without 
any  difference  of  locality.  When  a  compound  colour 
falls  upon  the  retina,  we  are  conscious  of  three  separate 
elementary  impressions,  probably  conveyed  by  separate 
nerves,  without  any  power  of  distinguishing  them.  We 
hear  in  a  note  struck  on  a  stringed  instrument  or  in  the 
human  voice,  different  tones  at  the  same  time,  one  fun- 
damental, and  a  series  of  harmonic  overtones,  which  also 
are  probably  received  by  different  nerves,  and  yet  we  are 
unable  to  separate  them  in  space.  IMany  articles  of  food 
produce  a  different  impression  of  taste  upon  different 
parts  of  the  tongue,  and  also  produce  sensations  of  odour 
by  their  volatile  particles  ascending  into  the  nostrils 
from  behind.  But  these  different  sensations,  recognised 
by  different  parts  of  the  nervous  system,  are  usually 
completely  and  inseparably  united  in  the  compound  sen- 
sation which  we  call  taste. 

No  doubt,  with  a  little  attention  it  is  possible  to 
ascertain  the  parts  of  the  body  which  receive  these  sen- 
sations, but,  even  when  these  are  known  to  be  locally 
separate,  it  does  not  follow  that  we  must  conceive  of  the 
sources  of  these  sensations  as  separated  in  the  same 
way. 

We  find  a  corresponding  fact  in  the  physiology  of  sight 
— namely,  that  we  see  only  a  single  object  with  our  two 
eyes,  although  the  impression  is  convej^ed  by  two  distinct 
nerves.  In  fact,  both  phenomena  are  examj)les  of  a  more 
universal  law. 

Hence,  when  we  find  that  a  plane  optical  image  of  the 
objects  in  the  field  of  vision  is  produced  on  the  retina, 
and  that  the  different  parts  of  this  image  excite  different 
fibres  of  the  optic  nerve,  this  is  not  a  sufficient  ground 
for  our  referring  the  sensations  thus  produced  to  locally 
distinct  regions  of  our  field  of  vision.     Something  else 


THE   PERCEPTION   OF   SIGHT.  27  3 

must  clearly  be  added  to  produce  the  notion  of  separation 
in  space. 

The  sense  of  touch  offers  precisely  the  same  problem. 
When  two  different  parts  of  the  skin  are  touched  at  the 
same  time,  two  different  sensitive  nerves  are  excited,  but 
the  local  separation  between  these  two  nerves  is  not  a 
sufficient  ground  for  our  recognition  of  the  two  parts 
which  have  been  touched  as  distinct,  and  for  the  concep- 
tion of  two  different  external  objects  which  follows. 
Indeed,  this  conception  will  vary  according  to  circum- 
stances. If  we  touch  the  table  with  two  fingers,  and  feel 
under  each  a  grain  of  sand,  we  suppose  that  there  are  two 
separate  grains  of  sand ;  but  if  we  place  the  two  fingers 
one  against  the  other,  and  a  grain  of  sand  between  them, 
we  may  have  the  same  sensations  of  touch  in  the  same 
two  nerves  as  before,  and  yet,  under  these  circumstancf  5, 
we  suppose  that  there  is  only  a  single  grain.  In  this  case, 
our  consciousness  of  the  position  of  the  fingers  has  ob- 
viously an  influence  upon  the  result  at  which  the  mind 
arrives.  This  is  further  proved  by  the  experiment  of 
crossing  two  fingers  one  over  the  other,  and  putting  a 
marble  between  them,  when  the  single  object  will  produce 
in  the  mind  the  conception  of  two. 

What,  then,  is  it  which  comes  to  help  the  anatomical 
distinction  in  locality  between  the  different  sensitive 
nerves,  and,  in  cases  like  those  I  have  mentioned,  produces 
the  notion  of  separation  in  space  ?  In  attempting  to 
answer  this  question,  we  cannot  avoid  a  controversy  which 
has  not  yet  been  decided. 

Some  physiologists,  following  the  lead  of  Johannes 
Miiller,  would  answer  that  the  retina  or  skin,  being  itself 
an  organ  which  is  extended  in  space,  perceives  impressions 
which  carry  with  them  this  quality  of  extension  in  space ; 


274  hecext  trogress  of  the  theory  of  vision. 

that  this  conception  of  locality  is  innate ;  and  that  im- 
pressions derived  from  external  objects  are  transmitted  of 
themselves  to  corresponding  local  positions  in  the  image 
produced  in  tli^  sensitive  organ.  We  may  describe  this  as 
the  Innate  or  Intuitive  Theory  of  conceptions  of  Space. 
It  obviously  cuts  short  all  further  enquiry  into  the  origin 
of  these  conceptions,  since  it  regards  them  as  some- 
thing original,  inborn,  and  incapable  of  further  explana- 
tion. 

The  opposing  view  was  put  forth  in  a  more  general 
form  by  the  early  English  philosophers  of  the  sensational 
school — by  Molyneux,^  Locke,  and  Jurin.^  Its  applica- 
tion to  special  physiological  problems  has  only  become 
possible  in  very  modern  times,  particularly  since  we  have 
gained  more  accurate  knowledge  of  the  movements  of  the 
eye.  The  invention  of  the  stereoscope  by  Wheatstone 
(p.  284)  made  the  difficulties  and  imperfections  of  the 
Innate  Theory  of  sight  much  more  obvious  than  before, 
and  led  to  another  solution  which  approached  much 
nearer  to  the  older  view,  and  which  we  will  call  the 
Empirical  Theory  of  Vision.  This  assumes  that  none  of 
our  sensations  give  us  anything  more  than  '  signs  '  for  ex- 
ternal objects  and  movements,  and  that  we  can  only  learn 
how  to  interpret  these  signs  by  means  of  experience  and 
practice.  For  example,  the  conception  of  differences  in 
locality  can  only  be  attained  by  means  of  movement,  and, 
in  the  field  of  vision,  depends  upon  our  experience  of  the 
movements  of  the  eye.  Of  course,  this  Empirical  Theory 
must  assume  a  difference  between  the  sensations  of 
various  parts  of  the  retina,  depending  upon  their  local 

»  William  Molyneux,  author  of  Dioptrica  Xova,  was  born  in  Dublin,  1656, 
and  died  in  the  same  city,  1698. 

2  James  Jurin,  M.D.,  Sec.  R.  S.,  physician  to  Guy's  Hospital,  and  Presi- 
dent of  the  Royal  Collfge  of  Physicians,  was  born  in  1684,  and  died  in  1760. 
Beside  works  on  the  Contraction  of  the  Heart,  on  Vis  viva,  &c.,  he  pub- 
lished, in  17.38,  a  treatise  on  District  and  Indistinct  Vision. — Ts. 


THE   PERCEPTION   OF   SIGHT.  275 

difference.  If  it  were  not  so,  it  would  be  impossible  to 
distinguish  any  local  difference  in  the  field  of  vision.  The 
sensation  of  red,  when  it  falls  upon  the  right  side  of  the 
retina,  must  in  some  way  be  different  from  the  sensation 
of  the  same  red  when  it  affects  the  left  side ;  and,  more- 
over, this  difference  between  the  two  sensations  must  be 
of  another  kind  from  that  which  we  recognise  when  the 
same  spot  in  the  retina  is  successively  affected  by  two 
different  shades  of  red.  Lotze  ^  has  named  this  difference 
between  the  sensations  which  the  same  colour  excites 
when  it  affects  different  parts  of  the  retina,  the  local  sign 
of  the  sensation.  We  are  for  the  present  ignorant  of  the 
nature  of  this  difference,  but  I  adopt  the  name  given  by 
Lotze  as  a  convenient  expression.  While  it  would  be 
premature  to  form  any  further  hypothesis  as  to  the 
nature  of  these  *  local  signs,'  there  can  be  no  doubt 
of  their  existence,  for  it  follows  from  the  fact  that  we 
are  able  to  distinguish  local  differences  in  the  field  of 
vision. 

The  difference,  therefore,  between  the  two  opposing 
views  is  as  follows.  The  Empirical  Theory  regards  the 
local  signs  (whatever  they  really  may  be)  as  signs  the 
signification  of  which  must  be  learnt,  and  is  actually 
learnt,  in  order  to  arrive  at  a  knowledge  of  the  external 
world.  It  is  not  at  all  necessary  to  suppose  any  kind  of 
correspondence  between  these  local  signs  and  the  actual 
differences  of  locality  which  they  signify.  The  Innate 
Theory,  on  the  other  hand,  supposes  that  the  local  signs 
are  nothing  else  than  direct  conceptions  of  differences 
in  space  as  such,  both  in  their  nature  and  their  magni- 
tude. 

'  Eudolf  Hermann  Lotze,  Professor  in  the  University  of  Gottingen, 
originally  a  disciple  of  Herbart  (v.  supra),  author  of  Allgemeine  Fhysiologie 
des  menschlichen  Korpers,  1851. — Te. 

13 


276     RECENT   PROGRESS   OF   THE   THEORY   OF   VISION. 

The  reader  will  see  how  the  subject  of  our  present 
enquiry  involves  the  consideration  of  that  far-reaching 
opposition  between  the  system  of  philosophy  which  as- 
sumes a  pre-existing  harmony  of  the  laws  of  mental 
operations  with  those  of  the  outer  world,  and  the  system 
which  attempts  to  derive  all  correspondence  between 
mind  and  matter  from  the  results  of  experience. 

So  long  as  we  confine  ourselves  to  the  observation  of  a 
field  of  two  dimensions,  the  individual  parts  of  which 
offer  no,  or,  at  any  rate,  no  recognisable,  difference  in 
their  distances  from  the  eye — so  long,  for  instance,  as 
we  only  look  at  the  sky  and  distant  parts  of  the  land- 
scape, both  the  above  theories  practically  offer  an  equally 
good  explanation  of  the  way  in  which  we  form  concep- 
tions of  local  relations  in  the  field  of  vision.  The  extension 
of  the  retinal  image  corresponds  to  the  extension  of  the 
actual  image  presented  by  the  objects  before  us ;  or,  at 
all  events,  there  are  no  incongruities  which  may  not  be 
reconciled  with  the  Innate  Theory  of  sight  without  any 
very  difficult  assumptions  or  explanations. 

The  first  of  these  incongruities  is  that  in  the  retinal 
picture  the  top  and  bottom  and  the  right  and  left  of  the 
actual  image  are  inverted.  This  is  seen  in  Fig.  30  to 
result  from  the  rays  of  light  crossing  as  they  enter  the 
pupil ;  the  point  a  is  the  retinal  image  of  A,  b  of  B. 
This  has  always  been  a  difficulty  in  the  theory  of  vision, 
and  many  hypotheses  have  been  invented  to  explain  it. 
Two  of  these  have  survived.  We  may,  with  Johannes 
Muller,  regard  the  conception  of  upper  and  lower  as  only 
a  relative  distinction,  so  far  as  sight  is  concerned — that 
is,  as  only  affecting  the  relation  of  the  one  to  the  other; 
and  we  must  further  suppose  that  the  feeling  of  corre- 
spondence between  what  is  upper  in  the  sense  of  sight  and 
in   the    sense  of  touch   is  only  acquired  by  experience. 


THE   PEECEPTION   OF  SIGHT.  277 

when  we  see  the  hands,  which  feel,  moving  in  the  field  of 
vision.  Or,  secondly,  we  may  assume  with  Fick  ^  that, 
since  all  impressions  upon  the  retina  must  be  conveyed  to 
the  brain  in  order  to  be  there  perceived,  the  nerves  of 
siglit  and  those  of  feeling  are  so  arranged  in  the  brain  as 
to  produce  a  correspondence  between  the  notions  they 
suggest  of  upper  and  under,  right  and  left.  This  sup- 
position has,  however,  no  pretence  of  any  anatomical  facts 
to  support  it. 

The  second  difficulty  for  the  Intuitive  Theory  is  that, 
while  we  have  two  retinal  pictures,  we  do  not  see  double. 
This  difficulty  was  met  by  the  assumption  that  both  retinse 
when  they  are  excited  produce  only  a  single  sensation  in 
the  brain,  and  that  the  several  points  of  each  retina  corre- 
spond with  each  other,  so  that  each  pair  of  corresponding  or 
'  identical '  points  produces  the  sensation  of  a  single  one. 
Now  there  is  an  actual  anatomical  arrangement  which 
might  perhaps  support  this  hypothesis.  The  two  optic 
nerves  cross  before  entering  the  brain,  and  thus  become 
united.  Pathological  observations  make  it  probable  that 
the  nerve-fibres  from  the  right-hand  halves  of  both  retinae 
pass  to  the  right  cerebral  hemisphere,  those  from  the  left 
halves  to  the  left  hemisphere.'*  But  although  correspond- 
ing nerve-fibres  would  thus  be  brought  close  together,  it 
has  not  yet  been  shown  that  they  actually  unite  in  the 
brain. 

'  Liidwng  Fick,  late  Professor  of  Medicine  in  the  University  of  Marburg, 
the  brother  of  Prof.  Adolf  Fick,  of  Ziirich. 

"^  We  may  compare  the  arrangement  to  that  of  the  reins  of  a  pair  of 
horses  :  the  inner  fibres  only  of  each  optic  nerve  cross,  so  that  those  which 
run  to  the  right  half  of  the  brain  are  the  outer  fibres  of  the  right  and  the 
inner  of  the  left  retina,  while  those  which  run  to  the  left  cerebral  hemi- 
sphere are  the  outer  fibres  of  the  left  and  the  inner  of  the  rifiht  retina  : 
just  as  the  inner  reins  of  both  horses  cross,  so  that  the  outer  rein  of  the  off 
horse  and  the  inner  of  the  near  one  run  together  to  the  driver's  right  hand, 
while  the  inner  rein  of  the  off  and  the  outer  of  the  near  horse  pass  to  his 
left  hand.— Te. 


278    RECEXT   PROGRESS    OF   THE   THEORY   OF   VISION. 

These  two  difficulties  do  not  apply  to  the  Empirical 
Theory,  since  it  only  supposes  that  the  actual  sensible 
'  sign,'  whether  it  be  simple  or  complex,  is  recognised  as 
the  sign  of  that  which  it  signifies.  An  uninstructed 
person  is  as  sure  as  possible  of  the  notions  he  derives 
from  his  eyesight,  without  ever  knowing  that  he  has  two 
retinae,  that  there  is  an  inverted  picture  on  each,  or  that 
there  is  such  a  thing  as  an  optic  nerve  to  be  excited,  or  a 
brain  to  receive  the  impression.  He  is  not  troubled  by 
his  retinal  images  being  inverted  and  double.  He  knows 
what  impression  such  and  such  an  object  in  such  and 
such  a  position  makes  on  him  through  his  eyesight, 
and  governs  himself  accordingly.  But  the  possibility  of 
learning  the  signification  of  the  local  signs  which  belong 
to  our  sensations  of  sight,  so  as  to  be  able  to  recognise 
the  actual  relations  which  they  denote,  depends,  first,  on 
our  having  movable  parts  of  our  own  body  within  sight ; 
so  that,  when  we  once  know  by  means  of  touch  what  rela- 
tion in  space  and  what  movement  is,  we  can  further 
learn  what  changes  in  the  impressions  on  the  eye  cor- 
respond to  the  voluntary  movements  of  a  hand  which  we 
can  see.  In  the  second  place,  when  we  move  our  eyes 
while  looking  at  a  field  of  vision  filled  with  objects  at 
rest,  the  retina,  as  it  moves,  changes  its  relation  to  the 
almost  unchanged  position  of  the  retinal  picture.  We 
thus  learn  what  impression  the  same  object  makes  upon 
different  parts  of  the  retina.  An  unchanged  retinal 
picture,  passing  over  the  retina  as  the  eye  turns,  is  like  a 
pair  of  compasses  which  we  move  over  a  drawing  in  order 
to  measure  its  parts.  Even  if  the  'local  signs'  of  sensa- 
tion were  quite  arbitrary,  thrown  together  without  any 
systematic  arrangement  (a  supposition  which  I  regard  as 
improbable),  it  would  still  be  possible  by  means  of  the 
movements  of  the  hand  and  of  the  eye,  as  just  described, 


THE   PERCEPTION   OF   SIGHT.  279 

to  ascertain  whicli  signs  go  together,  and  which  correspond 
in  different  regions  of  the  retina  to  points  at  similar 
distances  in  the  two  dimensions  of  the  field  of  vision. 
This  is  in  accordance  with  experiments  by  Fechner,^ 
Volkmann,'^  and  myself,  which  prove  that  even  the  fully 
developed  eye  of  an  adult  can  only  accurately  compare 
the  size  of  those  lines  or  angles  in  the  field  of  vision,  the 
images  of  which  can  be  thrown  one  after  another  upon 
precisely  the  same  spot  of  the  retina  by  means  of  the 
ordinary  movements  of  the  eye. 

Moreover,  we  may  convince  ourselves  by  a  simple  ex- 
periment that  the  harmonious  results  of  the  perceptions 
of  feeling  and  of  sight  depend,  even  in  the  adult,  upon  a 
constant  comparison  of  the  two,  by  means  of  the  retinal 
pictures  of  our  hands  as  they  move.  If  we  put  on  a  pair 
of  spectacles  with  prismatic  glasses,  the  two  flat  surfaces 
of  which  converge  towards  the  right,  all  objects  appear  to 
be  moved  over  to  the  right.  If  we  now  try  to  touch  any- 
thing we  see,  taking  care  to  shut  the  eyes  before  the  hand 
appears  in  sight,  it  passes  to  the  right  of  the  object ;  but 
if  we  follow  the  movement  of  the  hand  with  the  eye,  we 
are  able  to  touch  what  we  intend,  by  bringing  the  retinal 
image  of  the  hand  up  to  that  of  the  object.  Again,  if 
we  handle  the  object  for  one  or  two  minutes,  watching 
it  all  the  time,  a  fresh  correspondence  is  formed  between 
the  eye  and  the  hand,  in  spite  of  the  deceptive  glass, 
so  that  we  are  now  able  to  touch  the  object  with  per- 
fect certainty,  even  when  the  eyes  are  shut.  And  we 
can  even  do  the  same  with  the  other  hand  without  seeing 
it,  which  proves  that  it  is  not  the  perception  of  touch 

'  Gustav  Theodor  Fechner,  author  of  Elemente  der  Psychophysik,  1860  ; 
also  known  as  a  satirist. — Tb. 

"^  Alfred   Wilhelm  Volkmann,   s\iccessive1y  Professor  of  Physiology   at  . 
Leipzig.   Dorpat,  and  Halle;  author  oi Physiologische  JJnters'uchungen  im 
Gehiete  der  Ojptik,  1864,  &c.— Tb. 


280   RECENT   PROGRESS    OF   THE   THEORY   OF   VISION. 

which  has  been  rectified  by  comparison  with  the  false 
retinal  images,  but,  on  the  contrary,  the  perception  of 
sight  which  has  been  corrected  by  that  of  touch.  But, 
again,  if,  after  trying  this  experiment  several  times,  we 
take  off  the  spectacles  and  then  look  at  any  object,  taking 
care  not  to  bring  our  hands  into  the  field  of  vision,  and 
now  try  to  touch  it  with  our  eyes  shut,  the  hand  will  pass 
beyond  it  on  the  opposite  side  —that  is,  to  the  left.  The 
new  harmony  which  was  established  between  the  percep- 
tions of  sight  and  of  touch  continues  its  effects,  and  thus 
leads  to  fresh  mistakes  when  the  normal  conditions  are 
restored. 

In  preparing  objects  with  needles  under  a  compound 
microscope,  we  must  learn  to  harmonise  the  inverted  mi- 
croscopical image  with  our  muscular  sense ;  and  we  have 
to  get  over  a  similar  difficulty  in  shaving  before  a  look- 
ing-glass, which  changes  right  to  left. 

These  instances,  in  which  the  image  presented  in  the 
two  dimensions  of  the  field  of  vision  is  essentially  of  the 
same  kind  as  the  retinal  images,  and  resembles  them,  can 
be  equally  well  explained  (or  nearly  so)  by  the  two  oppo- 
site theories  of  vision  to  which  I  have  referred.  But  it  is 
quite  another  matter  when  we  pass  to  the  observation  of 
near  objects  of  three  dimensions.  In  this  case  there  is  a 
thorough  and  complete  incongruity  between  our  retinal 
images  on  the  one  hand,  and,  on  the  other,  the  actual 
condition  of  the  objects  as  well  as  the  correct  impression 
of  them  which  we  receive.  Here  we  are  compelled  to 
choose  between  the  two  opposite  theories,  and  accordingly 
this  department  of  our  subject — the  explanation  of  our 
Perception  of  Solidity  or  Depth  in  the  field  of  vision,  and 
that  of  binocular  vision  on  which  the  former  chiefly 
depends — has  for  many  years  become  the  field  of  much 
investigation  and  no  little  controversy.     And  no  won- 


THE   PERCEPTION   OF   SIGHT.  281 

der,  for  we  have  already  learned  enough  to  see  that  the 
questions  which  have  here  to  be  decided  are  of  funda- 
mental importance,  not  only  for  the  physiology  of  sight, 
but  for  a  correct  understanding  of  the  true  nature  and 
limits  of  human  knowledge  generally. 

Each  of  our  eyes  projects  a  plane  image  upon  its  own 
retina.  However  we  may  suppose  the  conducting  nerves 
to  be  arranged,  the  two  retinal  images  when  united  in 
the  brain  can  only  reappear  as  a  plane  image.  But 
instead  of  the  two  plane  retinal  images,  we  find  that 
the  actual  impression  on  our  mind  is  a  solid  image  of 
three  dimensions.  Here,  again,  as  in  the  system  of 
colours,  the  outer  world  is  richer  than  our  sensation  by 
one  dimension  ;  but  in  this  case  the  conception  formed 
by  the  mind  completely  represents  the  reality  of  the 
outer  world.  It  is  important  to  remember  that  this 
perception  of  depth  is  fully  as  vivid,  direct,  and  exact 
as  that  of  the  plane  dimensions  of  the  field  of  vision. 
If  a  man  takes  a  leap  from  one  rock  to  another,  his  life 
depends  just  as  much  upon  his  rightly  estimating  the 
distance  of  the  rock  on  which  he  is  to  alight,  as  upon 
his  not  misjudging  its  position,  right  or  left;  and,  as 
a  matter  of  experience,  we  find  that  we  can  do  the  one 
just  as  quickly  and  as  surely  as  the  other. 

In  what  way  can  this  appreciation  of  what  we  call 
depth,  solidity,  and  direct  distance  come  about  ?  Let 
us  first  ascertain  what  are  the  facts. 

At  the  outset  of  the  enquiry  we  must  bear  in  mind 
that  the  perception  of  the  solid  form  of  objects  and 
of  their  relative  distance  from  us  is  not  quite  absent, 
even  when  we  look  at  them  with  only  one  eye  and 
without  changing  our  position.  Now  the  means  which 
we  possess  in  this  case  are  just  the  same  as  those  which 
the  painter  can  employ  in  order  to  give  the  figures  on 
his  canvas  the  appearance  of  being  solid  objects,  and  of 


282    RECEXT   PEOGRESS   OF   THE   THEORY   OF   YISIOX. 

standing  at  diiSferent  distances  from  the  spectator.  It  is 
part  of  a  painter's  merit  for  his  figures  to  stand  out 
boldly.  Now  how  does  he  produce  the  illusion?  We 
shall  find,  in  the  first  place,  that  in  painting  a  landscape 
he  likes  to  have  the  sun  near  the  horizon,  which  gives 
him  strong  shadows ;  for  these  throw  objects  in  the 
foreground  into  bold  relief.  Next  he  prefers  an  atmo- 
sphere which  is  not  quite  clear,  because  slight  obscurity 
makes  the  distance  appear  far  off.  Then  he  is  fond  of 
bringing  in  figures  of  men  and  cattle,  because,  by  help  of 
these  objects  of  known  size,  we  can  easily  measure  the 
size  and  distance  of  other  parts  of  the  scene.  Lastly, 
houses  and  other  regular  productions  of  art  are  also 
useful  for  giving  a  clue  to  the  meaning  of  the  picture, 
since  they  enable  us  easily  to  recognise  the  position  of 
horizontal  surfaces.  The  representation  of  solid  forms 
by  drawings  in  correct  perspective  is  most  successful  in 
the  case  of  objects  of  regular  and  symmetrical  shape, 
such  as  buildings,  machines,  and  implements  of  various 
kinds.  For  we  know  that  all  of  these  are  chiefly  bounded 
either  by  planes  which  meet  at  a  right  angle  or  by 
spherical  and  cylindrical  surfaces  ;  and  this  is  sufficient 
to  supply  what  the  drawing  does  not  directly  show. 
Moreover,  in  the  case  of  figures  of  men  or  animals,  our 
knowledge  that  the  two  sides  are  symmetrical  further 
assists  the  impression  conveyed. 

But  objects  of  unknown  and  irregular  shape,  as  rocks 
or  masses  of  ice,  baffle  the  skill  of  the  most  consummate 
artist ;  and  even  their  representation  in  the  most  com- 
plete and  perfect  manner  possible,  by  means  of  photo- 
graphy, often  shows  nothing  but  a  confused  mass  of 
black  and  white.  Yet,  when  we  have  these  objects  in 
reality  before  our  eyes,  a  single  glance  is  enough  for 
us  to  recognise  their  form. 

The   first  who    clearly    showed   in   what   points   it    is 


THE  PERCEPTIOJf  OF  SIGHT.  283 

impossible  for  any  picture  to  represent  actual  objects  was 
the  great  master  of  painting,  Leonardo  da  Vinci,^  who 
was  almost  as  distinguished  in  natural  philosophy  as  in 
art.  He  pointed  out  in  his  Trattato  della  Plttura^  that 
the  views  of  the  outer  world  presented  by  each  of  our 
eyes  are  not  precisely  the  same.  Each  eye  sees  in  its 
retinal  image  a  perspective  view  of  the  objects  which 
lie  before  it ;  but,  inasmuch  as  it  occupies  a  somewhat 
different  position  in  space  from  the  other,  its  point 
of  view  and  so  its  whole  perspective  image  is  dif- 
ferent. If  T  hold  up  my  finger  and  look  at  it  first 
with  the  right  and  then  with  the  left  eye,  it  covers, 
in  the  picture  seen  })y  the  latter,  a  part  of  the  opposite 
wall  of  the  room  which  is  more  to  the  right  than  in 
the  picture  seen  by  the  right  eye.  If  I  hold  up  my  right 
hand  with  the  thumb  towards  me,  I  see  with  the  right 
eye  more  of  the  back  of  the  hand,  with  the  left  more 
of  the  palm  ;  and  the  same  effect  is  produced  whenever 
we  look  at  bodies  of  which  the  several  parts  are  at 
different  distances  from  our  eyes.  But  when  I  look  at  a 
hand  represented  in  the  same  position  in  a  painting,  the 
right  eye  will  see  exactly  the  same  figure  as  the  left,  and 
just  as  much  of  either  the  palm  or  the  back  of  it.  Thus 
we  see  that  actual  solid  objects  present  different  pictures 
to  the  two  eyes,  while  a  painting  shows  only  tlie  same. 
Hence  follows  a  difference  in  the  impression  made  upon 
the  sight  which  the  utmost  perfection  in  a  representation 
on  a  flat  surface  cannot  supply. 

The  clearest  proof  that  seeing  with  two  eyes,  and  the 
difference  of  the   pictures  presented  by  each,  constitute 

'  Born  at  Vinci,  near  Florence,  1452  ;  died  at  Cloux,  near  Amboise,  1519. 
Mr.  Hallam  says  of  his  scientific  writings,  that  they  are  'more  like  revela- 
tions of  physical  truths  vouchsafed  to  a  single  mind,  than  the  super- 
structure of  its  reasoning  upon  any  established  basis.  .  .  .  He  first  laid 
down  the  grand  principle  of  Bacon,  that  experiment  and  observation  must 
be  the  guides  to  just  theory  in  the  investigation  of  nature.' — Tb. 


284     RECENT   PHOGRESS   OP  THE   THEORY   OP   VISION. 

the  most  important  cause  of  our  perception  of  a  third 
dimension  in  the  field  of  vision,  has  been  furnished  by 
Wheatstone's  invention  of  the  stereoscope.^  I  may  assume 
that  this  instrument  and  the  peculiar  illusion  which  it 
produces  are  well  known.  By  its  help  we  see  the  solid 
shape  of  the  objects  represented  on  the  stereoscopic 
slide,  with  the  same  complete  evidence  of  the  senses  with 
which  we  should  look  at  the  real  objects  themselves. 
This  illusion  is  produced  by  presenting  somewhat  dif- 
ferent pictures  to  the  two  eyes — to  the  right,  one  which 
represents  the  object  in  perspective  as  it  would  appear 
to  that  eye,  and  to  the  left  one  as  it  would  appear  to  the 
left.  If  the  pictures  are  otherwise  exact  and  drawn  from 
two  different  points  of  view  corresponding  to  the  position 
of  the  two  eyes,  as  can  be  easily  done  by  photography,  we 
receive  on  looking  into  the  stereoscope  precisely  the  same 
impression  in  black  and  white  as  the  object  itself  would 
give. 

Anyone  who  has  sufficient  control  over  the  movements 
of  his  eyes  does  not  need  the  help  of  an  instrument  in 
order  to  combine  the  two  pictiu:es  on  a  stereoscopic  slide 
into  a  single  solid  image.  It  is  only  necessary  so  to 
direct  the  eyes,  that  each  of  them  shall  at  the  same  time 
see  corresponding  points  in  the  two  pictures ;  but  it  is 
easier  to  do  so  by  help  of  an  instrument  which  will 
apparently  bring  the  two  pictures  to  the  same  place. 

In  Wheatstone's  original  stereoscope,  represented  in 
Fig.  35,  the  observer  looked  with  the  right  eye  into  the 
mirror  6,  and  wdth  the  left  into  the  mirror  a.  Both 
mirrors  were  placed  at  an  angle  to  the  observer's  line  of 
sight,  and  the  two  pictures  were  so  placed  at  k  and  g 
that  their  reflected  images  appeared  at  the  same  place 
behind   the  two   mirrors ;    but   the    right   eye    saw   the 

*  Described  in  the  Philosophical  Transactions  for  1838. — Tb. 


THE   PERCEPTION   OF   SIGHT. 


285 


picture  g  in  the  mirror  6,  while  the  left  saw  the  picture 
k  in  the  mirror  a. 

A   more  convenient  instrument,  though    it   does   not 

Fig.  35. 


give  such  sharply  defined  effects,  is  tlie  ordinary  stereo- 
scope of  Brewster,^   shown   in  Fig.   36.     Here  the  two 


Fig.  36. 


pictures  are  placed  on  the  same  slide  and  laid  in  the 

'  Sir  David  Brewster,  Professor  of  Mathematics  at  Edinburgh,  born 
1781,  died  1868.— Tr. 


286     RECENT   PROGRESS   OF   THE   THEORY   OF   VISION. 

lower  part  of  the  stereoscope,  which  is  divided  by  a 
partition  s.  Two  slightly  prismatic  glasses  with  convex 
surfaces  are  fixed  at  the  top  of  the  instrument  which 
show  the  pictures  somewhat  further  off,  somewhat  mag- 
nified, and  at  the  same  time  overlapping  each  other, 
so  that  both  appear  to  be  in  the  middle  of  the  instru- 
ment. The  section  of  the  double  eye-piece  shown  in 
Fig.  37  exhibits  the  position  and  shape  of  the  right  and 
left  prisms.  Thus  both  pictures  are  apparently  brought 
to  the  same  spot,  and  each  eye  sees  only  the  one  which 
belongs  to  it. 


The  illusion  produced  by  the  stereoscope  is  most 
obvious  and  striking  when  other  means  of  recognising 
the  form  of  an  object  fail.  This  is  the  case  with  geo- 
metrical outlines  of  solid  figures,  such  as  diagrams  of 
crystals,  and  also  with  representations  of  irregular  objects, 
especially  when  they  are  transparent,  so  that  the  shadows 
do  not  fall  as  we  are  accustomed  to  see  them  in  opaque 
objects.  Thus  glaciers  in  stereoscopic  photographs  often 
appear  to  the  unassisted  eye  an  incomprehensible  chaos 
of  black  and  white,  but  when  seen  through  a  stereoscope 
the  clear  transparent  ice,  with  its  fissures  and  polished 
surfaces,  comes  out  as  if  it  were  real.  It  has  often 
happened  that  when  I  have  seen  for  the  first  time  build- 
ings, cities  or  landscapes,  with  which  I  was  familiar 
from  stereoscopic  pictures,  they  seemed  familiar  to 
me  ;  but  I  never  experienced  this  impression  after  see- 
ing any  number  of  ordinary  pictures,  because  these 
but  so  imperfectly  represent  the  real  effect  upon  the 
senses. 


THE   PERCEPTION"   OF   SIGHT.  287 

The  accuracy  of  the  stereoscope  is  no  less  wonderful. 
Dove  ^  has  contrived  an  ingenious  illustration  of  this. 
Take  two  pieces  of  paper  printed  with  the  same  type,  or 
from  the  same  copper-plate,  and  hence  exactly  alike,  and 
put  them  in  the  stereoscope  in  place  of  the  two  ordinary 
photographs.  They  will  then  unite  into  a  single  com- 
pletely flat  image,  because,  as  we  have  seen  above,  the 
two  retinal  images  of  a  flat  picture  are  identical.  But 
no  human  skill  is  able  to  copy  the  letters  of  one  cop- 
perplate on  to  another  so  perfectly  that  there  shall  not 
be  some  difference  between  them.  If,  therefore,  we  print 
off  the  same  sentence  from  the  original  plate  and  a  copy 
of  it,  or  the  same  letters  with  different  specimens  of  the 
same  type,  and  put  the  two  pieces  of  paper  into  the  ste- 
reoscope, some  lines  will  appear  nearer  and  some  further 
off  than  the  rest.  This  is  the  easiest  way  of  detecting 
spurious  bank  notes.  A  suspected  one  is  put  in  a  stereo- 
scope along  with  a  genuine  specimen  of  the  same  kind, 
and  it  is  then  at  once  seen  whether  all  the  marks  in  the 
combined  image  appear  on  the  same  plane.  This  ex- 
periment is  also  important  for  the  theory  of  vision,  since 
it  teaches  us  in  a  most  striking  manner  how  vivid,  sure, 
and  minute  is  our  judgment  as  to  depth  derived  from 
the  combination  of  the  two  retinal  images. 

We  now  come  to  the  question  how  is  it  possible  for 
two  different  flat  perspective  images  upon  the  retina, 
each  of  them  representing  only  two  dimensions,  to  com- 
bine so  as  to  present  a  solid  image  of  three  dimen- 
sions. 

'  Heinrich  "Wilhelm  Dove,  Professor  in  the  University  of  Berlin,  author 
of  Optische  Studien  (1859);  also  eminent  for  his  researches  in  meteorology 
and  electricity. 

His  paper,  Anwendung  des  StereosJcops  umfalschea  von  echtcm  Papiergcld 
zu  unterscheiden,  was  published  in  1859. — Tb. 


288     RECENT   PROGRESS   OF   THE   THEORY   OF   VISION. 

We  must  first  make  sure  that  we  are  really  able  to 
distinguish  between  the  two  flat  images  offered  us  by 
our  eyes.  If  I  hold  my  finger  up  and  look  towards  the 
opposite  wall,  it  covers  a  different  part  of  the  wall  to 
each  eye,  as  I  mentioned  above.  Accordingly  I  see  the 
finger  twice,  in  front  of  two  different  places  on  the  wall ; 
and  if  I  see  a  single  image  of  the  wall  I  must  see  a  double 
image  of  the  finger. 

Now  in  ordinary  vision  we  try  to  recognise  the  solid 
form  of  surrounding  objects,  and  either  do  not  notice  this 
double  image  at  all,  or  only  when  it  is  unusually  striking. 
In  order  to  see  it  we  must  look  at  the  field  of  vision 
in  another  way — in  the  way  that  an  artist  does  who 
intends  to  draw  it.  He  tries  to  forget  the  actual  shape, 
size,  and  distance  of  the  objects  that  he  represents.  One 
would  think  that  this  is  the  more  simple  and  original 
way  of  seeing  things  ;  and  hitherto  most  physiologists 
have  regarded  it  as  the  kind  of  vision  which  results 
most  directly  from  sensation,  while  they  have  looked  on 
ordinary  solid  vision  as  a  secondary  way  of  seeing  things, 
which  has  to  be  learned  as  the  result  of  experience.  But 
every  draughtsman  knows  liow  much  harder  it  is  to 
appreciate  the  apparent  form  in  which  objects  appear 
in  the  field  of  vision,  and  to  measure  the  angular 
distance  between  them,  than  to  recognise  what  is  their 
actual  form  and  comparative  size.  In  fact,  the  knowledge 
of  the  true  relations  of  surrounding  objects  of  which  the 
artist  cannot  divest  himself,  is  his  greatest  difficulty  in 
drawing  from  nature. 

Accordingly,  if  we  look  at  the  field  of  vision  with  both 
eyes,  in  the  way  an  artist  does,  fixing  our  attention  upon  the 
outlines,  as  they  would  appear  if  projected  on  a  pane 
of  glass  between  us  and  them,  we  then  become  at  once 
aware  of  the  difference  between  the  two  retinal  images. 
We  see  those  objects  double  which   lie   further    off  or 


THE   PERCEPTION   OF   SIGHT.  289 

nearer  than  the  point  at  which  we  are  looking,  and  are 
not  too  far  removed  from  it  laterally  to  admit  of  their 
position  being  sufficiently  seen.  At  first  we  can  only 
recognise  double  images  of  objects  at  very  different 
distances  from  the  eye,  but  by  practice  they  will  be  seen 
with  objects  at  nearly  the  same  distance. 

All  these  phenomena,  and  others  like  them,  of  double 
images  of  objects  seen  with  both  eyes,  may  be  reduced 
to  a  simple  rule  which  was  laid  down  by  Johannes 
Miiller : — '  For  each  point  of  one  retina  there  is  on  the 
other  a  corresponding  point.'  In  the  ordinary  flat  field 
of  vision  presented  by  the  two  e}es,  the  images  received 
by  corresponding  points  as  a  rule  coincide,  while  images 
received  by  those  which  do  not  correspond  do  not  co- 
incide. The  corresponding  points  in  each  retina  (without 
noticing  slight  deviations)  are  those  which  are  situated 
at  the  same  lateral  and  vertical  distance  from  the  point 
of  the  retina  at  which  rays  of  light  come  to  a  focus  when 
we  fix  the  eye  for  exact  vision,  namely,  the  yellow  spot. 

The  reader  will  remember  that  the  intuitive  theory 
of  vision  of  necessity  assumes  a  complete  combination 
of  those  sensations  which  are  excited  by  impressions 
upon  corresponding,  or,  as  Miiller  calls  them,  '  identical ' 
points.  This  supposition  was  most  fully  expressed  in 
the  anatomical  hypothesis,  that  two  nerve  fibres  which 
arise  from  corresponding  points  of  the  two  retinae  actually 
unite  so  as  to  form  a  single  fibre,  either  at  the  commissure 
of  the  optic  nerves  or  in  the  brain  itself.  I  may,  how- 
ever, remark  that  Johannes  Miiller  did  not  definitely 
commit  himself  to  this  mechanical  explanation,  although 
he  suggested  its  possibility.  He  wished  his  law  of  iden- 
tical points  to  be  regarded  simply  as  an  expression  of 
facts,  and  only  insisted  that  the  position  in  the  field  of 
vision  of  the  images  they  receive  is  always  the  same. 

But  a  difficulty  arose.     The  distinction    between   the 


290     RECENT   PROGRESS   OF   THE   THEORY   OF   VISIOJ^. 

double  images  is  comparatively  imperfect,  whenever  it  is 
possible  to  combine  them  into  a  single  view  ;  a  striking 
contrast  to  the  extraordinary  precision  with  which,  as 
Dove  has  shown,  we  can  judge  of  stereoscopic  relief.  Yet 
the  latter  power  depends  upon  ths  same  differences  between 
the  two  retinal  pictures  which  cause  the  phenomenon  of 
double  images.  The  slight  difference  of  distance  between 
the  objects  represented  in  the  right  and  left  half  of  a 
stereoscopic  photograph,  which  suffices  to  produce  the 
most  striking  effect  of  solidity,  must  be  increased  twenty 
or  thirty-fold  before  it  can  be  recognised  in  the  produc- 
tion of  a  double  image,  even  if  we  suppose  the  most 
careful  observation  by  one  who  is  well  practised  in  the 
experiment. 

Again,  there  are  a  number  of  other  circumstances  which 
make  the  recognition  of  double  images  either  easy  or 
difficult.  The  most  striking  instance  of  the  latter  is  the 
effect  of  relief.  The  more  vivid  the  impression  of  solidity, 
the  more  difficult  are  double  images  to  see,  so  that 
it  is  easier  to  see  them  in  stereoscopic  pictures  than 
in  the  actual  objects  they  represent.  On  the  other  hand, 
the  observation  of  double  images  is  facilitated  by  varying 
the  colour  and  brightness  of  the  lines  in  the  two  stereo- 
scopic pictures,  or  by  putting  lines  in  both  which  exactly 
correspond,  and  so  will  make  more  evident  by  contrast 
the  imperfect  coalescence  of  the  other  lines.  All  these 
circumstances  ought  to  have  no  influence,  if  the  com- 
bination of  the  two  images  in  our  sensation  depended 
upon  any  anatomical  arrangement  of  the  conducting 
nerves. 

Again,  after  the  invention  of  the  stereoscope,  a 
fresh  difficulty  arose  in  explaining  our  perceptions  of 
solidity  by  the  differences  between  the  two  retinal 
images.      First,   Briicke '    called   attention   to   a   series 

*  Professor  of  Physiology  in  the  University  of  Vienna. 


THE   PERCEPTION   OF   SIGHT.  291 

of  facts  which  apparently  made  it  possible  to  reconcile 
the  new  phenomena  discovered  with  the  theory  of  the 
innate  identity  of  the  sensations  conveyed  by  the  two 
retinae.  If  we  carefully  follow  the  way  in  which  we 
look  at  stereoscopic  pictures  or  at  real  objects,  we 
notice  that  the  eye  follows  the  different  outlines  one 
after  another,  so  that  we  see  the  '  fixed  point '  at  each 
moment  single,  while  the  other  points  appear  double. 
But,  usually,  our  attention  is  concentrated  upon  the 
fixed  point,  and  we  observe  the  double  images  so  little 
that  to  many  people  they  are  a  new  and  surprising  phe- 
nomenon when  first  pointed  out.  Now  since  in  following 
the  outlines  of  these  pictures,  or  of  an  actual  image,  we 
move  the  eyes  unequally  this  way  and  that,  sometimes 
they  converge,  and  sometimes  diverge,  according  as  we 
look  at  points  of  the  outline  which  are  apparently  nearer 
or  further  off;  and  these  differences  in  movement  may 
give  rise  to  the  impression  of  different  degrees  of  distance 
of  the  several  lines. 

Now  it  is  quite  true,  that  by  this  movement  of  the 
eye  while  looking  at  stereoscopic  outlines,  we  gain  a 
much  more  clear  and  exact  image  of  the  raised  surface 
they  represent,  than  if  we  fix  our  attention  upon  a  single 
point.  Perhaps  the  simple  reason  is  that  when  we  move 
the  eyes  we  look  at  every  point  of  the  figure  in  suc- 
cession directly^  and  therefore  see  it  much  more  sharply 
defined  than  when  we  see  only  one  point  directly  and  the 
others  indirectly.  But  Briicke's  hypothesis,  that  the 
perception  of  solidity  is  only  produced  by  this  movement 
of  the  eyes,  was  disproved  by  experiments  made  by  Dove, 
which  showed  that  the  peculiar  illusion  of  stereoscopic 
pictures  is  also  produced  when  they  are  illuminated 
with  an  electric  spark.  The  light  then  lasts  for  less 
than  the  four  thousandth  part  of  a  second.  In  this 
time  heavy  bodies  move  so  little,  even  at  great  velocities. 


292     RECE]^   PROGRESS    OF    THE    THEORY   OF   VISION. 

that  they  seem  to  be  at  rest.  Hence  there  cannot  be  the 
slightest  movement  of  the  eye,  while  the  spark  lasts, 
which  can  possibly  be  recognised  ;  and  yet  we  receive 
the  complete  impression  of  stereoscopic  relief. 

Secondly,  such  a  combination  of  the  sensations  of 
the  two  eyes  as  the  anatomical  hypothesis  assumes,  is 
proved  not  to  exist  by  the  phenomenon  of  stereoscopic 
lustre,  which  was  also  discovered  by  Dove.  If  the  same 
surface  is  made  white  in  one  stereoscopic  picture  and 
black  in  another,  the  combined  image  appears  to  shine, 
though  the  paper  itself  is  quite  dull.  Stereoscopic  draw- 
ings of  crystals  are  made  so  that  one  shows  white  lines 
on  a  black  ground,  and  the  other  black  lines  on  a  white 
ground.  When  looked  at  through  a  stereoscope  they  give 
the  impression  of  a  solid  crystal  of  shining  graphite.  By 
the  same  means  it  is  possible  to  produce  in  stereoscopic 
photographs  the  still  more  beautiful  effect  of  the  sheen 
of  water  or  of  leaves. 

The  explanation  of  this  curious  phenomenon  is  as 
follows : — A  dull  surface,  like  unglazed  white  paper, 
reflects  the  light  which  falls  on  it  equally  in  all  direc- 
tions, and,  therefore,  always  looks  equally  bright,  from 
whatever  point  it  is  seen  ;  hence,  of  course,  it  appears 
equally  bright  to  both  eyes.  On  the  other  hand,  a 
polished  surface,  beside  the  reflected  light  which  it 
scatters  equally  in  all  directions,  throws  back  other  beams 
by  regular  reflection,  which  only  pass  in  definite  directions. 
Now  one  eve  may  receive  this  regularly  reflected  light 
and  the  other  nut ;  the  surface  will  then  appear  much 
brighter  to  the  one  than  to  the  other,  and,  as  this  can  only 
happen  with  shining  bodies,  the  effect  of  the  black  and 
white  stereoscopic  pictures  appears  like  that  of  a  poli^^hed 
surface. 

Now  if  there  were  a  complete  combination  of  the 
impressions  produced   upon  both  retinae,  the  union   of 


THE    PERCEPTION    OF   SIGHT.  293 

white  and  black  would  give  grey.  The  fact,  therefore, 
that  when  they  are  actually  combined  in  the  stereoscope 
they  produce  the  effect  of  lustre,  that  is  to  say,  an 
effect  which  cannot  be  produced  by  any  kind  of  uniform 
grey  surface,  proves  that  the  impressions  on  the  two 
retinae  are  not  combined  into  one  sensation. 

That,  again,  this  effect  of  stereoscopic  lustre  does  not 
depend  upon  an  alternation  between  the  perceptions 
of  the  two  eyes,  on  what  is  called  the  '  rivalry  of  the 
retinae,'  is  proved  by  illuminating  stereoscopic  pictures 
for  an  instant  with  the  electric  spark.  The  same  effect 
is  perfectly  produced. 

In  the  third  place,  it  can  be  proved,  not  only  that  the 
images  received  by  the  two  eyes  do  not  coalesce  in  our 
sensation,  but  that  the  two  sensations  which  we  receive 
from  the  two  eyes  are  not  exactly  similar,  that  they  can, 
on  the  contrary,  be  readily  distinguished.  For  if  the  sen- 
sation given  by  the  right  eye  were  indistinguishably  the 
same  as  that  given  by  the  left,  it  would  follow  that,  at 
least  in  the  case  of  the  electric  spark  (when  no  movements 
of  the  eye  can  help  us  in  distinguishing  the  two  images), 
it  would  make  no  difference  whether  we  saw  the  right 
hand  stereoscopic  picture  with  the  right  eye,  and  the  left 
with  the  left,  or  put  the  two  pictures  into  the  stereo- 
scope reversed,  so  as  to  see  that  intended  for  the  right 
eye  with  the  left,  and  that  intended  for  the  left  eye 
with  the  right.  -  But  practically  we  find  that  it  makes 
all  the  difference,  for  if  we  make  the  two  pictures  change 
places,  the  relief  appears  to  be  inverted  :  what  should  be 
further  off  seems  nearer,  what  should  stand  out  seems 
.to  fall  back.  Now,  since  when  we  look  at  objects  by 
the  momentary  light  of  the  electric  spark,  they  always 
appear  in  their  true  relief  and  never  reversed,  it  follows 
that  the  impression  produced  on  the  right  eye  is  not 
indistinguishable  from  that  on  the  left. 


294     RECENT   PROGRESS   OF   THE   THEORY   OF  VISION. 

Lastly,  there  are  some  very  curious  and  interesting 
phenomena  seen  when  two  pictures  are  put  before  the 
two  eyes  at  the  same  time  which  cannot  be  combined  so 
as  to  present  the  appearance  of  a  single  object.  If,  for 
example,  we  look  with  one  eye  at  a  page  of  print,  and 
with  the  other  at  an  engraving,^  there  follows  what  is 
called  the  '  rivalry '  of  the  two  fields  of  vision.  The  two 
images  are  not  then  seen  at  the  same  time,  one  covering 
the  other ;  but  at  some  points  one  prevails,  and  at  others 
the  other.  If  they  are  equally  distinct,  the  places  where 
one  or  the  other  appears  usually  change  after  a  few 
seconds.  But  if  the  engraving  presents  anywhere  in  the 
field  of  vision  a  uniform  white  or  black  surface,  then 
the  printed  letters  which  occupy  the  same  position  in  the 
image  presented  to  the  other  eye,  will  usually  prevail 
exclusively  over  the  uniform  surface  of  the  engraving.  In 
spite,  however,  of  what  former  observers  have  said  to  the 
contrary,  I  maintain  that  it  is  possible  for  the  observer  at 
any  moment  to  control  this  rivalry  by  voluntary  direction 
of  his  attention.  If  he  tries  to  read  the  printed  sheet,  the 
letters  remain  visible,  at  least  at  the  spot  where  for  the 
moment  he  is  reading.  If,  on  the  contrary,  he  tries  to 
follow  the  outline  and  shadows  of  the  engraving,  then 
these  prevail.  I  find,  moreover,  that  it  is  possible  to  fix 
the  attention  upon  a  very  feebly  illuminated  object,  and 
make  it  prevail  over  a  much  brighter  one,  which  coincides 
with  it  in  the  retinal  image  of  the  other  eye.  Thus,  I 
can  follow  the  watermarks  of  a  white  piece  of  paper  and 
cease  to  see  strongly-marked  black  figures  in  the  other 
field.  Hence  the  retinal  rivalry  is  not  a  trial  of  strength 
between   two  sensations,  but   depends   upon   our   fixing 

'  The  practised  observer  is  able  to  do  this  without  any  apparatus,  but 
most  persons  will  find  it  necessary  to  put  the  two  objects  in  a  stereoscope 
or,  at  least,  to  hold  a  book,  or  a  sheet  of  paper,  or  the  hand  in  front  of  the 
face,  to  serve  for  the  partition  in  the  stereoscope. — Tu. 


THE   PERCEPTIOX   OF   SIGHT.  295 

on  failing  to  fix  the  attention.  Indeed  there  is  scarcely 
any  phenomenon  so  well  fitted  for  the  study  of  the  causes 
which  are  capable  of  determining  the  attention.  It  is  not 
enough  to  form  the  conscious  intention  of  seeing  first 
with  one  eye  and  then  with  the  other ;  we  must  form  as 
clear  a  notion  as  possible  of  what  we  expect  to  see.  Then 
it  will  actually  appear.  If,  on  the  other  hand,  we  leave 
the  mind  at  liberty  without  a  fixed  intention  to  ob- 
serve a  definite  object,  that  alternation  between  the  two 
pictures  ensues  which  is  called  retinal  rivalry.  In  this 
case,  we  find  that,  as  a  rule,  bright  and  strongly  marked 
objects  in  one  field  of  vision  prevail  over  those  which 
are  darker  and  less  distinct  in  the  other,  either  com- 
pletely or  at  least  for  a  time. 

We  may  vary  this  experiment  by  using  a  pair  of 
spectacles  with  different  coloured  glasses.  We  shall  then 
find,  on  looking  at  the  same  objects  with  both  eyes 
at  once,  that  there  ensues  a  similar  rivalry  between  the 
two  colours.  Everything  appears  spotted  over  first  with 
one  and  then  with  the  other.  After  a  time,  however,  the 
vividness  of  both  colours  becomes  weakened,  partly  by 
the  elements  of  the  retina  which  are  affected  by  each  of 
them  being  tired,  and  partly  by  the  complementary 
after-images  which  result.  The  alternation  then  ceases, 
and  there  ensues  a  kind  of  mixture  of  the  two  original 
colours. 

It  is  much  more  difficult  to  fix  the  attention  upon  a 
colour  than  upon  such  an  object  as  an  engraving.  For  the 
attention  upon  which,  as  we  have  seen,  the  whole  phe- 
nomenon of  '  rivalry  '  depends,  fixes  itself  with  constancy 
only  upon  such  a  picture  as  continually  offers  something 
new  for  the  eye  to  follow.  But  we  may  assist  this  by 
reflecting  on  the  side  of  the  glasses  next  the  eye  letters 
or  other  lines  upon  which  the  attention  can  fix.  These 
reflected  images  themselves  are  not  coloured,  but  as  soon 


296     RECENT   PROGRESS   OF   THE   THEORY   OF   VISION. 

as  the  attention  is  fixed  upon  one  of  them  we  become 
conscious  of  the  colour  of  the  corresponding  glass. 

These  experiments  on  the  rivalry  of  colours  have  given 
rise  to  a  singular  controversy  among  the  best  observers  ; 
and  the  possibility  of  such  difference  of  opinion  is  an 
instructive  hint  as  to  the  nature  of  the  phenomenon 
itself.  One  party,  including  the  names  of  Dove,  Reg- 
nault,^  Briicke,  Ludwig,^  Panum,^  and  Hering,^  main- 
tains that  the  result  of  a  binocular  view  of  two  colours 
is  the  true  combination-colour.  Other  observers,  as 
Heinrich  Meyer  of  Ziirich,  Yolkm^ann,  Meissner,^  and 
Funke,^  declare  quite  as  positively  that,  under  these 
conditions,  they  have  never  seen  the  combination-colour. 
I  myself  entirely  agree  with  the  latter,  and  a  careful 
examination  of  the  cases  in  which  I  might  have  imagined 
that  I  saw  tlie  combination-colour,  has  always  proved  to 
me  that  it  was  the  result  of  phenomena  of  contrast. 
Each  time  that  I  brought  the  true  combination-colour 
side  by  side  with  the  binocular  mixture  of  colours,  the 
difference  between  the  two  was  very  apparent.  On  the 
other  hand,  there  can  of  course  be  no  doubt  that  the  ob- 
servers I  first  naDied  really  saw  what  they  profess,  so  that 
there  mast  here  be  great  individual  difference.  Indeed 
with  certain  experiments  which  Dove  recommends  as  par- 
ticularly well  fitted  to  prove  the  correctness  of  his  con- 
clusion, such  as  the  binocular  combination  of  comple- 
mentary polarisation-colours  into  white,  I  could  not 
myself  see  the  slightest  trace  of  a  combination-colour. 

'  The  distinguished  French  chemist,  father  of  the  well-known  painter 
who  was  killed  in  the  second  siege  of  Paris. 

*  Professor  of  Physiology  in  the  University  of  Leipzig. 
'  Professor  of  Physiology  in  the  University  of  Kiel. 

*  Ewald  Hering,  Professor  of  Physiology  in  the  University  of  Prague, 
lately  in  the  Josephsakademie  of  Vienna. 

*  Professor  of  Physiology  in  the  University  of  Gottingen. 

*  Professor  of  Physiology  in  the  University  of  Freiburg. — Tk. 


THE   PERCEPTION   OF   SIGHT.  297 

This  striking  difference  in  a  comparatively  simple 
observation  seems  to  me  to  be  of  great  interest.  It  is  a 
remarkable  confirmation  of  the  supposition  above  made, 
in  accordance  with  the  empirical  theory  of  vision,  that  in 
general  only  those  sensations  are  perceived  as  separated 
in  space,  which  can  be  separated  one  from  another  by 
voluntary  movements.  Even  when  we  look  at  a  compound 
colour  with  one  eye,  only  three  separate  sensations  are,  ac- 
cording to  Young's  theory,  produced  together ;  but  it  is 
impossible  to  separate  these  by  any  movement  of  the 
eye,  so  that  they  always  remain  locally  united.  Yet  we 
have  seen  that  even  in  this  case  we  may  become  conscious 
of  a  separation  under  certain  circumstances;  namely, 
when  it  is  seen  that  part  of  the  colour  belongs  to  a 
transparent  covering.  When  two  corresponding  points 
of  the  retinae  are  illuminated  with  different  colours,  it 
will  be  rare  for  any  separation  between  them  to  appear  in 
ordinary  vision ;  if  it  does,  it  will  usually  take  place  in 
the  part  of  the  field  of  sight  outside  the  region  of  exact 
vision.  But  there  is  always  a  possibility  of  separating 
the  compound  impression  thus  produced  into  its  two 
parts,  which  will  appear  to  some  extent  independent  of 
each  other,  and  will  move  with  the  movements  of  the 
eye;  and  it  will  depend  upon  the  degree  of  attention 
which  the  observer  is  accustomed  to  give  to  the  region 
of  indirect  vision  and  to  double  images,  whether  he 
is  able  to  separate  the  colours  which  fall  on  both  retinae 
at  the  same  time.  Mixed  hues,  whether  looked  at  with 
one  eye  or  with  both,  excite  many  simple  sensations 
of  colour  at  the  same  time,  each  having  exactly  the 
same  position  in  the  field  of  vision.  The  difference  in 
the  way  in  which  such  a  compound-colour  is  regarded 
by  different  people  depends  upon  whether  this  compound 
sensation  is  at  once  accepted  as  a  coherent  whole  without 
any  attempt  at  analysis,  or  whether  the  observer  is  able 


298     RECENT   PROGRESS   OF   THE   THEORY   OF   VISION. 

by  practice  to  recognise  the  parts  of  which  it  is  com- 
posed, and  to  separate  them  from  one  another.  The 
former  is  our  usual  (though  not  constant)  habit  when 
looking  with  one  eye,  while  we  are  more  inclined  to  the 
latter  when  using  both.  But  inasmuch  as  this  incli- 
nation must  chiefly  depend  upon  practice  in  observing 
distinctions,  gained  by  preceding  observation,  it  is  easy 
to  understand  how  great  individual  peculiarities  may 
arise. 

If  we  carefully  observe  the  rivalry  which  ensues  when 
we  try  to  combine  two  stereoscopic  drawings,  one  of  which 
is  in  black  lines  on  a   white  ground  and  the  other  in 
white  lines  on  black,  we  shall  see  that  the   white  and 
black  lines  which  affect  nearly  corresponding  points  of  each 
retina  always  remain  visible  side  by  side — an  effect  which 
of  course  implies  that  the  white  and  black  grounds  are 
also  visible.     By  this  means    the  brilliant  surface,  which 
seems  to  shine  like  black  lead,  makes  a  much  more  stable 
impression   than    that  produced  under   the  operation   of 
retinal    rivalry   by  entirely    different    drawings.      If  we 
cover  the  lower  half  of  the  white  figure  on  a  black  ground 
with  a  sheet  of  printed  paper,  the  upper  half  of  the  com- 
bined stereoscopic  image  shows  the  plienomenon  of  Lustre, 
while  in  the  lower  we  see  Eetinal  Eivalry  between  the 
black  lines  of  the   figure  and   the  black  marks  of  the 
type.     As  long  as  the  observer  attends  to  the  solid  form 
of  the  object  represented,  the  black  and  white  outlines 
of  the  two  stereoscopic  drawings  carry  on  in  common  the 
point  of  exact  vision  as  it  moves  along  them,  and  the 
effect  can  only  be  kept  up  by  continuing  to  follow  both. 
He  must  steadily  keep  his  attention  upon  both  drawings, 
and  then  the  impression  of  each  will  be  equally  combined. 
There  is  no  better  way  of  preserving  the  combined  effect 
of  two    stereoscopic   pictures    than    this.      Indeed   it   is 
possible  to  combine  (at  least   partially  and  for  a  short 


THE   PERCEPTION   OP   SIGHT.  299 

time)  two  entirely  different  drawings  when  put  into  the 
stereoscope,  by  fixing  the  attention  upon  the  way  in 
which  they  cover  each  other,  watching,  for  instance,  the 
angles  at  which  their  lines  cross.  But  as  soon  as  the 
attention  turns  from  the  angle  to  follow  one  of  the  lines 
which  makes  it,  the  picture  to  which  the  other  line 
belongs  vanishes 

Let  us  now  put  together  the  results  to  which  our 
inquiry  into  binocular  vision  has  led  us. 

I.  The  excitement  of  corresponding  points  of  the  two 
retinae  is  not  indistinguishably  combined  into  a  single 
impression ;  for,  if  it  were,  it  would  be  impossible  to  see 
Stereoscopic  Lustre.  And  we  have  found  reason  to  believe 
that  this  effect  is  not  a  consequence  of  Eetinal  Kivalry, 
even  if  we  admit  the  latter  phenomenon  to  belong  to 
sensation  at  all,  and  not  rather  to  the  degree  of  attention. 
On  the  contrary  the  appearance  of  lustre  is  associated 
with  the  restriction  of  this  rivalry. 

II.  The  sensations  which  are  produced  by  the  excita- 
tion of  corresponding  points  of  each  retina  are  not  in- 
distinguishably the  same ;  for  otherwise  we  should  not 
be  able  to  distinguish  the  true  from  the  inverted  or 
'  pseudoscopic  '  relief,  when  two  stereoscopic  pictures  are 
illuminated  by  the  electric  spark. 

III.  The  combination  of  the  two  different  sensations 
received  from  corresponding  retinal  points  is  not  pro- 
duced by  one  of  them  being  suppressed  for  a  time ; 
for,  in  the  first  place,  the  perception  of  solidity  given  by 
the  two  eyes  depends  upon  our  being  at  the  same  time 
conscious  of  the  two  different  images,  and,  in  the  second, 
this  perception  of  solidity  is  independent  of  any  move- 
ment of  the  retinal  images,  since  it  is  possible  under 
momentary  illumination. 

We  therefore  learn  that  two  distinct  sensations  are  trans- 
U 


300     RECENT   PROGRESS    OF   THE   THEORY   OF   VISION. 

mitted  from  the  two  eyes,  and  reach  the  consciousness 
at  the  same  time  and  without  coalescing  ;  that  accordingly 
the  combination  of  these  two  sensations  into  the  single 
picture  of  the  external  world  of  which  we  are  conscious 
in  ordinary  vision  is  not  produced  by  any  anatomical 
mechanism  of  sensation,  but  by  a  mental  act. 

IV.  Further,  we  find  that  there  is,  on  the  whole,  com- 
plete, or  at  least  nearly  complete,  coincidence  as  to 
localisation  in  the  field  of  vision  of  impressions  of  sight 
received  from  corresponding  points  of  the  retinae  ;  but 
that  when  we  refer  both  impressions  to  the  same  object, 
their  coincidence  of  localisation  is  much  disturbed. 

If  this  coincidence  were  the  result  of  a  direct  function 
of  sensation,  it  could  not  be  disturbed  by  the  mental 
operation  which  refers  the  two  impressions  to  the  same 
object.  But  we  avoid  the  difficulty,  if  we  suppose  that 
the  coincidence  in  localisation  of  the  corresponding 
pictures  received  from  the  two  eyes  depends  upon  the 
power  of  measuring  distances  at  sight  which  we  gain  by 
experience,  that  is,  on  an  acquired  knowledge  of  the 
meaning  of  the  '  signs  of  localisation.'  In  this  case  it  is 
simply  one  kind  of  experience  opposing  another  ;  and 
we  can  then  understand  how  the  conclusion  that  two 
images  belong  to  the  same  object  should  influence  our 
estimation  of  their  relative  position  by  the  measuring 
power  of  the  eye,  and  how  in  consequence  the  distance 
of  the  two  images  from  the  fixed  point  in  the  field  of 
vision  should  be  regarded  as  the  same,  although  it  is  not 
exactly  so  in  reality. 

But  if  the  practical  coincidence  of  corresponding  points 
as  to  localisation  in  the  two  fields  of  vision  does  not 
depend  upon  sensation,  it  follows  that  the  origioal  power 
of  comparing  different  distances  in  each  separate  field  of 
vision  cannot  depend  upon  direct  sensation.  For,  if  it 
were  so,  it  would  follow  that  the  coincidence  of  the  two 


THE   PERCEPTION   OF   SIGHT.  301 

fields  would  be  completely  established  by  direct  sensation, 
as  soon  as  the  observer  had  got  his  two  fixed  points  to 
coincide  and  a  single  raeridian  of  one  eye  to  coincide 
with  the  corresponding  one  of  the  other. 

The  reader  sees  how  this  series  of  facts  has  driven  us 
by  force  to  the  empirical  theory  of  vision.  It  is  right  to 
mention  that  lately  fresh  attempts  have  been  made  to 
explain  the  origin  of  our  perception  of  solidity  and  the 
phenomena  of  single  and  double  binocular  vision  by  the 
assumption  of  some  ready-made  anatomical  mechanism. 
We  cannot  criticise  these  attempts  here :  it  would  lead 
us  too  far  into  details.  Although  many  of  these  hypo- 
theses are  very  ingenious  (and  at  the  same  time  very 
indefinite  and  elastic),  they  have  hitherto  always  proved 
insufiicient ;  because  the  actual  world  offers  us  far  more 
numerous  relations  than  the  authors  of  these  attempts 
could  provide  for.  Hence,  as  soon  as  they  have  arranged 
one  of  their  systems  to  explain  any  particular  phe- 
nomenon of  vision,  it  is  found  not  to  answer  for  any 
other.  Then,  in  order  to  help  out  the  hypothesis, 
the  very  doubtful  assumption  has  to  be  made  that,  in 
these  other  cases,  sensation  is  overcome  and  extinguished 
by  opposing  experience.  But  what  confidence  could  we 
put  in  any  of  our  perceptions  if  we  were  able  to  extinguish 
our  sensations  as  we  please,  whenever  they  concern  an 
object  of  our  attention,  for  the  sake  of  previous  concep- 
tions to  which  they  are  opposed  ?  At  any  rate,  it  is  clear 
that  in  every  case  where  experience  must  finally  decide, 
we  shall  succeed  much  better  in  forming  a  correct  notion 
of  what  we  see,  if  we  have  no  opposing  sensations  to 
overcome,  than  if  a  correct  j  udgment  must  be  formed  in 
spite  of  them. 

It  follows  that  the  hypotheses  which  have  been  suc- 
cessively framed  by  the  various  supporters  of  intuitive 


302     RECENT   PROGRESS   OF   THE   THEORY   OF   VISION. 

theories  of  vision,  in  order  to  suit  one  phenomenon  after 
another,  are  really  quite  unnecessary.  No  fact  has 
yet  been  discovered  inconsistent  with  the  Empirical 
Theory:  which  does  not  assume  any  peculiar  modes 
of  physiological  action  in  the  nervous  system,  nor  any 
hypothetical  anatomical  structures ;  which  supposes  no- 
thing more  than  the  well  known  association  between  the 
impressions  we  receive  and  the  conclusions  we  draw  from 
them,  according  to  the  fundamental  laws  of  daily  ex- 
perience. It  is  true  that  we  cannot  at  present  offer  any 
complete  scientific  explanation  of  the  mental  operations 
involved,  and  there  is  no  immediate  prospect  of  our  doing 
so.  But  since  these  operations  actually  exist,  and  since 
hitherto  every  form  of  the  intuitive  theory  has  been 
obliged  to  fall  back  on  their  reality  when  all  other 
explanation  failed,  these  mysteries  of  the  laws  of  thought 
cannot  be  regarded  from  a  scientific  point  of  view  as  con- 
stituting any  deficiency  in  the  empirical  theory  of  vision. 

It  is  impossible  to  draw  any  line  in  the  study  of  our 
perceptions  of  space  which  shall  sharply  separate  those 
which  belong  to  direct  Sensation  from  those  which  are 
the  result  of  Experience.  If  we  attempt  to  draw  such 
a  boundary,  we  find  that  experience  proves  more  minute, 
more  direct  and  more  exact  than  supposed  sensation, 
and  in  fact  proves  its  own  superiority  by  overcoming  the 
latter.  The  only  supposition  which  does  not  lead  to  any 
contradiction  is  that  of  the  Empirical  Theory,  which 
regards  all  our  perceptions  of  space  as  depending  upon 
experience,  and  not  only  the  qualities,  but  even  the 
local  signs  of  the  sense  of  sight  as  nothing  more  than 
signs,  the  meaning  of  which  we  have  to  learn  by  ex- 
perience. 

We  become  acquainted  with  their  meaning  by  com- 
paring them  with  the  result  of  our  own  movements,  with 


THE    PERCEPTION    OF   SIGHT.  303 

the  changes  which  we  thus  produce  in  the  outer  world. 
The  infant  first  begins  to  play  with  its  hands.  There  is 
a  time  when  it  does  not  know  how  to  turn  its  eyes  or 
its  hands  to  an  object  which  attracts  its  attention  by  its 
brightness  or  colour.  When  a  little  older,  a  child  seizes 
whatever  is  presented  to  it,  turns  it  over  and  over  again, 
looks  at  it,  touches  it,  and  puts  it  in  his  mouth.  The 
simplest  objects  are  what  a  child  likes  best,  and  he 
always  prefers  the  most  primitive  toy  to  the  elaborate 
inventions  of  modern  ingenuity.  After  he  has  looked  at 
such  a  toy  every  day  for  weeks  together,  he  learns  at  last 
all  the  perspective  images  which  it  presents ;  then  he 
throws  it  away  and  wants  a  fresh  toy  to  handle  like  the 
first.  By  this  means  the  child  learns  to  recognise  the 
different  views  which  the  same  olject  can  afford,  in 
connection  with  the  movements  which  he  is  constantly 
giving  it.  The  conception  of  the  shape  of  any  object, 
gained  in  this  manner,  is  the  result  of  associating  all 
these  visual  images.  When  we  have  obtained  an  accurate 
conception  of  the  form  of  any  object,  we  are  then  able 
to  imagine  what  appearance  it  would  present,  if  we  looked 
at  it  from  some  other  point  of  view.  All  these  different 
views  are  combined  in  the  judgment  we  form  as  to  the 
dimensions  and  shape  of  an  object.  And,  consequently, 
when  we  are  once  acquainted  with  this,  we  can  deduce 
from  it  the  various  images  it  would  present  to  the  sight 
when  seen  from  different  points  of  view,  and  the  various 
movements  which  we  should  have  to  impress  upon  it  in 
order  to  obtain  these  successive  images. 

I  have  often  noticed  a  striking  instance  of  what  I  have 
been  saying  in  looking  at  stereoscopic  pictures.  If,  for 
example,  we  look  at  elaborate  outlines  of  complicated 
crystalline  forms,  it  is  often  at  first  difficult  to  see  what 
they  mean.     When  this  is  the  case,  I  look  out  two  points 


304     RECEXT   PROGEESS    OP   THE   THEORY   OF   VISION. 

in  the  diagram  which  correspond,  and  make  them  overlap 
by  a  volmitary  movement  of  the  eyes.  But  as  long  as  I 
have  not  made  out  what  kind  of  form  the  drawings  are  in- 
tended to  represent,  I  find  that  ray  eyes  begin  to  diverge 
again,  and  the  two  points  no  longer  coincide.  Then  I  try 
to  follow  the  different  lines  of  the  figure,  and  suddenly  I 
see  what  the  form  represented  is.  From  that  moment  my 
two  eyes  pass  over  the  outlines  of  the  apparently  solid 
body  with  the  utmost  ease,  and  without  ever  separating. 
As  soon  as  we  have  gained  a  correct  notion  of  the  shape 
of  an  object,  we  have  the  rule  for  the  movements  of  the 
eyes  which  are  necessary  for  seeing  it.  In  carrying  out 
these  movements,  and  thus  receiving  the  visual  impres- 
sions we  expect,  we  retranslate  the  notion  we  have  formed 
into  reality,  and  by  finding  this  retranslation  agrees  with 
the  original,  we  become  convinced  of  the  accuracy  of  our 
conception. 

This  last  point  is,  I  believe,  of  great  importance. 
The  meaning  we  assign  to  our  sensations  depends  upon 
experiment,  and  not  upon  mere  observation  of  what  takes 
place  around  us.  We  learn  by  experiment  that  the  cor- 
respondence between  two  processes  takes  place  at  any 
moment  that  we  choose,  and  under  conditions  which  we 
can  alter  as  we  choose.  Mere  observation  would  not  give 
us  the  same  certainty,  even  though  often  repeated  under 
different  conditions.  For  we  should  thus  only  learn  that 
the  processes  in  question  appear  together  frequently  (or 
even  always,  as  far  as  our  experience  goes)  ;  but  mere 
observation  would  not  teach  us  that  they  appear  together 
at  any  moment  we  select. 

Even  in  considering  examples  of  scientific  observation, 
methodically  carried  out,  as  in  astronomy,  meteorology, 
or  geology,  we  never  feel  fully  convinced  of  the  causes  of 
the  phenomena  observed  until  we  can  demonstrate  the 
working  of  these  same  forces  by  actual  experiment  in 


THE   PEECEPTION   OF   SIGHT.  305 

the  laboratory.  So  long  as  science  is  not  experimental 
it  does  not  teach  us  the  knowledge  of  any  new  force.* 

It  is  plain  that,  by  the  experience  which  we  collect  in 
the  way  I  have  been  describing,  we  are  able  to  learn 
as  much  of  the  meaning  of  sensible  '  signs '  as  can 
afterwards  be  verified  by  further  experience ;  that  is  to 
say,  all  that  is  real  and  positive  in  our  conceptions. 

It  has  been  hitherto  supposed  that  the  sense  of  touch 
confers  the  notion  of  space  and  movement.  At  first 
of  course  the  only  direct  knowledge  we  acquire  is  that 
we  can  produce,  by  an  act  of  volition,  changes  of 
which  we  are  cognisant  by  means  of  touch  and  sight. 
Most  of  these  voluntary  changes  are  movements,  or 
changes  in  the  relations  of  space  ;  but  we  can  also  pro- 
duce changes  in  an  object  itself.  Now,  can  we  recognise 
the  movements  of  our  hands  and  eyes  as  changes  in  the 
relations  of  space,  without  knowing  it  beforehand  ?  and 
can  we  distinguish  them  from  other  changes  which  affect 
the  properties  of  external  objects  ?  I  believe  we  can.  It 
is  an  essentially  distinct  character  of  the  Eolations  of 
Space  that  they  are  changeable  relations  bettueen  objects 
which  do  not  depend  on  their  quality  or  quantity,  while  all 
other  material  relations  between  objects  depend  upon  their 
properties.  The  perceptions  of  sight  prove  this  directly 
and  easily.  A  movement  of  the  eye  which  causes  the 
retiral  image  to  shift  its  place  upon  the  retina  always 
produces  the  same  series  of  changes  as  often  as  it  is 
repeated,  whatever  objects  the  field  of  vision  may  con- 
tain. The  effect  is  that  the  impressions  which  had 
before  the  local  signs  a,,,  a^,  a^,  a^,  receive  the  new  local 
signs  60,  61,  62?  ^3  5  ^^d  this  may  always  occur  in  the  same 

*  An  interesting  paper,  applying  this  view  of  the  'experimental'  cha- 
racter of  progressive  science  to  Zoology,  has  been  published  by  M.  Lacaze 
Duthiers,  in  the  first  number  of  his  Archives  de  Zoologie. — Tb. 


306     RECENT   PROGRESS   OF   THE   THEORY   OF   VISION. 

way,  whatever  be  the  quality  of  the  impressions.  By 
this  means  we  learn  to  recognise  such  changes  as  be- 
longing to  the  special  phenomena  which  we  call  changes 
in  space.  This  is  enough  for  the  object  of  Empirical 
Philosophy,  and  we  need  not  further  enter  upon  a  dis- 
cussion of  the  question,  how  much  of  universal  concep- 
tions of  space  is  derived  a  prioH,  and  how  much  a 
posteriori  ?  ^ 

An  objection  to  the  empirical  Theory  of  Vision  might 
be  found  in  the  fact  that  illusions  of  the  senses  are 
possible ;  for  if  we  have  learnt  the  meaning  of  our 
sensations  from  experience,  they  ought  always  to  agree 
with  experience.  The  explanation  of  the  possibility  of 
illusions  lies  in  the  fact  that  we  transfer  the  notions 
of  external  objects,  which  would  be  correct  under  normal 
conditions,  to  cases  in  which  unusual  circumstances  have 
altered  the  retinal  pictures.  What  I  call  '  observation 
under  normal  conditions  '  implies  not  only  that  the  rays  of 
light  must  pass  in  straight  lines  from  each  visible  point 
to  the  cornea,  but  also  that  we  must  use  our  eyes  in  the 
way  they  should  be  used  in  order  to  receive  the  clearest 
and  most  easily  distinguishable  images.  This  implies 
that  we  should  successively  bring  the  images  of  the 
separate  points  of  the  outline  of  the  objects  we  are 
looking  at  upon  the  centres  of  both  retinse  (the  yellow 
spot),  and  also  move  the  eyes  so  as  to  obtain  the  surest 
comparison  between  their  various  positions.  When- 
ever we  deviate  from  these  conditions  of  normal  vision, 
illusions  are  the  result.  Such  are  the  long  recognised 
effects  of  the  refraction  or  reflection  of  rays  of  light 
before  they  enter  the  eye.     But  there  are  many  other 

*  The  question  of  the  origin  of  our  conceptions  of  space  is  discussed  by 
Mr.  Bain  on  empirical  principles  in  his  treatise  on  The  Se7iscs  and  tlie  In- 
tellect,  pp.  lU-118,  189-194,  245,  363-392,  &c.— Tb. 


THE  PEECEPTION   OF  SIGHT.  807 

causes  of  mistake  as  to  the  position  of  the  objects  we 
see — defective  accommodation  when  looking  through  one 
or  two  small  openings,  improper  convergence  when 
looking  with  one  eye  only,  irregular  position  of  the 
eye-ball  from  external  pressure  or  from  paralysis  of  its 
muscles.  Moreover,  illusions  may  come  in  from  certain 
elements  of  sensation  not  being  accurately  distinguished  ; 
as,  for  instance,  the  degree  of  convergence  of  the  two 
eyes,  of  which  it  is  difficult  to  form  an  accurate  judgment 
when  the  muscles  which  produce  it  become  fatigued. 

The  simple  rule  for  all  illusions  of  sight  is  this :  we 
always  believe  that  we  see  such  objects  as  luould,  under 
conditions  of  normal  vision,  'produce  the  retinal  image 
of  which  we  are  actually  conscious.  If  these  images  are 
such  as  could  not  be  produced  by  any  normal  kind  of 
observation,  we  judge  of  them  according  to  their  nearest 
resemblance;  and  in  forming  this  judgment,  we  more 
easily  neglect  the  parts  of  sensation  which  are  imperfectly 
than  those  which  are  perfectly  apprehended.  When  more 
than  one  interpretation  is  possible,  we  usually  waver 
involuntarily  between  them  ;  but  it  is  possible  to  end 
this  uncertainty  by  bringing  the  idea  of  any  of  the 
possible  interpretations  we  choose  as  vividly  as  possible 
before  the  mind  by  a  conscious  effort  of  the  will. 

These  illusions  obviously  depend  upon  mental  processes 
which  may  be  described  as  false  inductions.  But  there 
are,  no  doubt,  judgments  which  do  not  depend  upon 
our  consciously  thinking  over  former  observations  of  the 
same  kind,  and  examining  whether  they  justify  the 
conclusion  which  we  form.  I  have,  therefore,  named 
these  '  unconscious  judgments ; '  and  this  term,  though 
accepted  by  other  supporters  of  the  empirical  theory, 
has  excited  much  opposition,  because,  according  to 
generally-accepted    psychological   doctrines,  2,  judgment, 


308     BECENT   PROGRESS   OP   THE   THEORY   OP  VISION". 

or  logical  conclusion^  is  the  culminating  point  of  the 
conscious  operations  of  the  mind.  But  the  judgments 
which  play  so  great  a  part  in  the  perceptions  we  derive 
from  our  senses  cannot  be  expressed  in  the  ordinary 
form  of  logically  analysed  conclusions,  and  it  is  neces- 
sary to  deviate  somewhat  from  the  beaten  patlis  of  psy- 
chological analysis  in  order  to  convince  ourselves  that 
we  really  have  here  the  same  kind  of  mental  operation 
as  that  involved  in  conclusions  usually  recognised  as 
such.  There  appears  to  me  to  be  in  reality  only  a  super- 
ficial difference  between  the  '  conclusions '  of  logicians 
and  those  inductive  conclusions  of  which  we  recognise  the 
result  in  the  conceptions  we  gain  of  the  outer  world 
through  our  sensations.  The  difference  chiefly  depends 
upon  the  former  conclusions  being  capable  of  expression 
in  words,  while  the  latter  are  not ;  because,  instead  of 
words,  they  only  deal  with  sensations  and  the  memory 
of  sensf^ttions.  Indeed,  it  is  just  the  impossibility  of 
describing  sensations,  whether  actual  or  remembered,  in 
words,  which  makes  it  so  diflBcult  to  discuss  this  depart- 
ment of  psychology  at  all. 

Beside  the  knowledge  which  has  to  do  with  Notions, 
and  is,  therefore,  capable  of  expression  in  words,  there  is 
another  department  of  our  mental  operations,  which  may 
be  described  as  knowledge  of  the  relations  of  those 
impressions  on  the  senses  which  are  not  capable  of  direct 
verbal  expression.  For  instance,  when  we  say  that  we 
'  know '  ^  a  man,  a  road,  a  fruit,  a  perfume,  we  mean  that 
we  have  seen,  or  tasted,  or  smelt,  these  objects.  We 
keep  the  sensible  impression  fast  in  our  memory,  and  we 
shall   recognise   it   again   when   it  is  repeated,  but   we 

'  In  German  this  kind  of  knowledge  is  expressed  by  the  verb  hnnen 
(cognoacere,  co?inailre),  to  be  acquriinted  with,  while  tvissen  (scire,  savoir) 
means  to  be  aware  of^  The  former  kind  of  knowledge  is  only  applicable  to 
objects  directly  cognisable  by  the  senses,  whereas  the  latter  applies  to 
notions  or  conceptions  which  can  be  formally  stated  as  propositions. — Tb. 


THE   PERCEPTION   OF   SIGHT.  309 

cannot  describe  the  impression  in  words,  even  to  our- 
selves. And  yet  it  is  certain  that  this  kind  of  know- 
ledge {Kennen)  may  attain  the  highest  possible  degree 
of  precision  and  certainty,  and  is  so  far  not  inferior 
to  any  knowledge  {Wissen)  which  can  be  expressed  in 
words ;  but  it  is  not  directly  communicable,  unless  the 
object  in  question  can  be  brought  actually  forward,  or 
the  impression  it  produces  can  be  otherwise  represented 
— as  by  drawing  the  portrait  of  a  man  instead  of  pro- 
ducing the  man  himself. 

It  is  an  important  part  of  the  former  kind  of  know- 
ledge to  be  acquainted  with  the  particular  innervation  of 
muscles,  which  is  necessary  in  order  to  produce  any  eifect 
we  intend  by  moving  our  limbs.  As  children,  we  must 
learn  to  walk ;  we  must  afterwards  learn  how  to  skate  or 
go  on  stilts,  how  to  ride,  or  swim,  or  sing,  or  pronounce  a 
foreign  language.  Moreover,  observation  of  infants  shows 
that  they  have  to  learn  a  number  of  things  which  after- 
wards they  will  know  so  well  as  entirely  to  forget  that 
there  was  ever  a  time  when  they  were  ignorant  of  them. 
For  example,  everyone  of  us  had  to  learn,  when  an 
infant,  how  to  turn  his  eyes  toward  the  light  in  order  to 
see.  This  kind  of  'knowledge'  (Kennen)  we  also  call 
'  being  able '  to  do  a  thing  (kdnnen),  or  '  understanding  ' 
how  to  do  it  {verstehen\  as,  '  I  know  how  to  ride,' '  I  am 
able  to  ride,'  or  '  I  understand  how  to  ride.'  ^ 

It  is  important  to  notice  that  this  '  knowledge  '  of  the 
effort  of  the  will  to  be  exerted  must  attain  the  highest 
possible  degree  of  certainty,  accuracy,  and  precision,  for 
us  to  be  able  to  maintain  so  artificial  a  balance  as  is 
necessary  for  Avalking  on  stilts  or  for  skating,  for  the  singer 
to  know  how  to  strike  a   note   with   his  voice,   or   the 

^  The  German  word  konnen  is  said  to  be  of  the  same  etymology  as 
kcnmn,  and  so  their  likeness  in  form  would  be  explained  by  their  likeness 
in  meaning. 


310     KECEXT   PEOGRESS   OF   THE   THEORY   OF  YISIOX. 

violin-player  with  his  finger,  so  exactly  that  its  vibration 
shall  not  be  out  by  a  hundredth  part. 

Moreover,  it  is  clearly  possible,  by  using  these  sensible 
images  of  memory  instead  of  words,  to  produce  the  same 
kind  of  combination  which,  when  expressed  in  words, 
would  be  called  a  proposition  or  a  conclusion.  For 
example,  I  may  know  that  a  certain  person  with  whose 
face  I  am  familiar,  has  a  peculiar  voice,  of  which  I  have 
an  equally  lively  recollection.  I  should  be  able  with 
the  utmost  certainty  to  recognise  his  face  and  his  voice 
among  a  thousand,  and  each  would  recall  the  other.  But 
1  cannot  express  this  fact  in  words,  unless  I  am  able  to 
add  some  other  characters  of  the  person  in  question 
which  can  be  better  defined.  Then  I  should  be  able  to 
resort  to  a  syllogism  and  say,  '  This  voice  which  I  now 
hear  belongs  to  the  man  whom  I  saw  then  and  there.' 
But  imiversal,  as  well  as  particular  conclusions,  maybe 
expressed  in  terms  of  sensible  impressions,  instead  of 
words.  To  prove  this  I  need  only  refer  to  the  effect  of 
works  of  art.  The  statue  of  a  god  would  not  be 
capable  of  conveying  a  notion  of  a  definite  character  and 
disposition,  if  I  did  not  know  that  the  form  of  face  and 
the  expression  it  wears  have  usually  or  constantly  a  cer- 
tain definite  signification.  And,  to  keep  in  the  domain 
of  the  perceptions  of  the  senses,  if  I  know  that  a  par- 
ticular way  of  looking,  for  which  I  have  learnt  how  to 
employ  exactly  the  right  kind  of  innervation,  is  necessary 
in  order  to  bring  into  direct  vision  a  point  two  feet  off 
and  so  many  feet  to  the  right,  this  also  is  a  universal 
proposition  which  applies  to  every  case  in  which  I  have 
fixed  a  given  point  at  that  distance  before,  or  may  do  so 
hereafter.  It  is  a  piece  of  knowledge  which  cannot  be 
expressed  in  words,  but  is  the  result  which  sums  up  my 
previous  successful  experience.  It  may  at  any  moment 
become  the  major  premiss  of  a  syllogism,  whenever,  in 
fact,  I  fix  a  point  in  the  supposed  position  and  feel  that  I 


THE   PERCEPTION   OF   SIGHT.  311 

do  so  by  looking  as  that  major  proposition  states.  This 
perception  of  what  I  am  doing  is  my  minor  proposition, 
and  the  '  conclusion^  is  that  the  object  I  am  looking  for 
will  be  found  at  the  spot  in  question. 

Suppose  that  I  employ  the  same  way  of  looking,  but  look 
into  a  stereoscope.  I  am  now  aware  that  there  is  no  real 
object  before  me  at  the  spot  I  am  looking  at ;  but  I  have  the 
same  sensible  impression  as  if  one  were  there  ;  and  yet  I 
am  unable  to  describe  this  impression  to  myself  or  others, 
or  to  characterise  it  otherwise  than  as  '  the  same  impression 
which  would  arise  in  the  normal  method  of  observation,  if 
an  object  were  really  there.'  It  is  important  to  notice  this. 
No  doubt  the  physiologist  can  describe  the  impression 
in  other  ways,  by  the  direction  of  the  eyes,  the  position 
of  the  retinal  images,  and  so  on ;  but  there  is  no  other 
way  of  directly  defining  and  characterising  the  sensation 
which  we  experience.  Thus  we  may  recognise  it  as  an 
illusion,  but  yet  we  cannot  get  rid  of  the  sensation  of  this 
illusion  ;  for  we  cannot  extinguish  our  remembrance  of 
its  normal  signification,  even  when  we  know  that  in  the 
case  before  us  this  does  not  apply — just  as  little  as  we 
are  able  to  drive  out  of  the  mind  the  meaning  of  a 
word  in  our  mother  tongue,  when  it  is  employed  as  a 
sign  for  an  entirely  different  purpose. 

These  conclusions  in  the  domain  of  our  sensible  per- 
ceptions appear  as  inevitable  as  one  of  the  forces  of 
nature,  and  hence  their  results  seem  to  be  directly  ap- 
prehended, without  any  effort  on  our  part ;  but  this 
does  not  distinguish  them  from  logical  and  conscious 
conclusions,  or  at  least  from  those  which  really  deserve 
the  name.  All  that  we  can  do  by  voluntary  and  con- 
scious effort,  in  order  to  come  to  a  conclusion,  is,  after 
all,  only  to  supply  complete  materials  for  constructing  the 
necessary  premisses.  As  soon  as  this  is  done,  the  conclu- 
sion forces  itself  upon  us.     Those  conclusions  which  (it  is 


312     RECEXT   PROGRESS   OF   THE   THEORY   OF  VISION. 

supposed)  may  be  accepted  or  avoided  as  we  please,  are 
not  worth  much. 

The  reader  will  see  that  these  investigations  have  led 
us  to  a  field  of  mental  operations  which  has  been  seldom 
entered  by  scientific  explorers.  The  reason  is  that  it  is 
difficult  to  express  these  operations  in  words.  They  have 
been  hitherto  most  discussed  in  writings  on  aesthetics, 
where  they  play  an  important  part  as  Intuition,  Uncon- 
scious Eatiocination,  Sensible  Intelligibility,  and  such 
obscure  designations.  There  lies  under  all  these  phrases 
the  false  assumption  that  the  mental  operations  we  are 
discussing  take  place  in  an  undefined,  obscure,  half- 
conscious  fashion  ;  that  they  are,  so  to  speak,  mechanical 
operations,  and  thus  subordinate  to  conscious  thought, 
which  can  be  expressed  in  language.  I  do  not  l)elieve 
that  any  difference  in  kind  between  the  two  functions 
can  be  proved.  The  enormous  superiority  of  knowledge 
which  has  become  ripe  for  expression  in  language,  is 
sufficiently  explained  by  the  fact  that,  in  the  first  place, 
speech  makes  it  possible  to  collect  together  the  ex- 
perience of  millions  of  individuals  and  thousands  of 
generations,  to  preserve  them  safely,  and  by  continual 
verification  to  make  them  gradually  more  and  more 
certain  and  universal ;  while,  in  the  second  place,  all 
deliberately  combined  actions  of  mankind,  and  so  the 
greatest  part  of  human  power,  depend  on  language.  In 
neither  of  these  respects  can  mere  familiarity  with  phe- 
nomena {das  Kennen)  compete  with  the  knowledge  of 
them  which  can  be  communicated  by  speech  (das  Wis- 
sen) ;  and  yet  it  does  not  follow  of  necessity  that  the 
one  kind  of  knowledge  should  be  of  a  different  nature 
from  the  other,  or  less  clear  in  its  operation. 

The  supporters  of  Intuitive  Theories  of  Sensation  often 
appeal  to  the  capabilities  of  new-born  animals,  many  of 


THE   PERCEPTION   OF   SIGHT.  313 

which  show  themselves  much  more  skilful  than  a  human 
infant.  It  is  quite  clear  that  an  infant,  in  spite  of  the 
greater  size  of  its  brain,  and  its  power  of  mental  develop- 
ment, learns  with  extreme  slowness  to  perform  the 
simplest  tasks  ;  as,  for  example,  to  direct  its  eyes  to  an 
object  or  to  touch  what  it  sees  with  its  hands.  Must  we 
not  conclude  that  a  child  has  much  more  to  learn  than 
an  animal  which  is  safely  guided,  but  also  restricted, 
by  its  instincts  ?  It  is  said  that  the  calf  sees  the  udder 
and  goes  after  it,  but  it  admits  of  question  whether  it 
does  not  simply  smell  it,  and  make  those  movements 
which  bring  it  nearer  to  the  scent. ^  At  any  rate,  the 
child  knows  nothing  of  the  meaning  of  the  visual  image 
presented  by  its  mother's  breast.  It  often  turns  obsti- 
nately away  from  it  to  the  wrong  side  and  tries  to  find 
it  there.  The  young  chicken  very  soon  pecks  at  grains 
of  corn,  but  it  pecked  while  it  was  still  in  the  shell, 
and  when  it  hears  the  hen  peck,  it  pecks  again,  at  first 
seemingly  at  random.  Then,  when  it  has  by  chance  hit 
upon  a  grain,  it  may,  no  doubt,  learn  to  notice  the  field 
of  vision  which  is  at  the  moment  presented  to  it.  The 
process  is  all  the  quicker  because  the  whole  of  the  mental 
furniture  which  it  requires  for  its  life  is  but  small. 

We  need,  however,  further  investigations  on  the  sub- 
ject in  order  to  throw  light  upon  this  question.  As  far 
as  the  observations  with  which  I  am  acquainted  go,  they 
do  not  seem  to  me  to  prove  that  anything  more  than 
certain  tendencies  is  born  with  animals.  At  all  events 
one  distinction  between  them  and  man  lies  precisely  in 
this,  that  these  innate  or  congenital  tendencies,  im- 
pulses or  instincts  are  in  him  reduced  to  the  smallest 
possible  number  and  strength.^ 

'  See  Darwin  on  the  Expression  of  the  Emotiovs,  p.  47- — Tr. 
*  See  on  this  subject  Bain  on  the  Senses  and  the  Intellect,  p.  293  ;  also  a 
paper  on  'Instinct'  in  Nature,  Oct.  10,  1872. 


314     RECENT   PROGRESS    OF   THE   THEORY   OP   VISIOIT. 

There  is  a  most  striking  analogy  between  the  entire 
range  of  processes  which  we  have  been  discussing,  and 
another  System  of  Signs,  which  is  not  given  by  nature 
but  arbitrarily  chosen,  and  which  must  undoubtedly  be 
learned  before  it  is  understood.  I  mean  the  words  of  our 
mother  tongue. 

Learning  liow  to  speak  is  obviously  a  much  more 
difficult  task  than  acquiring  a  foreign  language  in  after 
life.  First,  the  child  has  to  guess  that  the  sounds  it 
hears  are  intended  to  be  signs  at  all ;  next,  the  meaning 
of  each  separate  sound  must  be  found  out,  by  the  same 
kind  of  induction  as  the  meaning  of  the  sensations  of 
sight  or  touch ;  and  yet  we  see  children  by  the  end 
of  their  first  year  already  understanding  certain  words 
and  phrases,  even  if  they  are  not  yet  able  to  repeat 
them.     We  may  sometimes  observe  the  same  in  dogs. 

Now  this  connection  between  Names  and  Objects,  which 
demonstrably  must  be  learnt^  becomes  just  as  firm  and 
indestructible  as  that  between  Sensations  and  the  Objects 
which  produce  them.  We  cannot  help  thinking  of  the 
usual  signification  of  a  word,  even  when  it  is  used 
exceptionably  in  some  other  sense  ;  we  cannot  help  feeling 
the  mental  emotions  which  a  fictitious  narrative  calls 
forth,  even  when  we  know  that  it  is  not  true ;  just  in  the 
same  way  as  we  cannot  get  rid  of  the  normal  signification 
of  the  sensations  produced  by  any  illusion  of  the  senses, 
even  when  we  know  that  they  are  not  real. 

There  is  one  other  point  of  comparison  which  is  worth 
notice.  The  elementary  signs  of  language  are  only  twenty- 
six  letters,  and  yet  what  wonderfully  varied  meanings 
can  we  express  and  communicate  by  their  combination ! 
Consider,  in  comparison  with  this,  the  enormous  number 
of  elementary  signs  with  which  the  machinery  of  sight 
is  provided.  We  may  take  the  number  of  fibres  in  the 
optic  nerves  as  two  hundred  and  fifty  thousand.     Each 


THE   FERCEPTION   OF   SIGHT.  315 

of  these  is  capable  of  innumerable  different  degrees  of 
sensation  of  one,  two,  or  three  primary  colours.  It 
follows  that  it  is  possible  to  construct  an  immeasurably 
greater  number  of  combinations  here  than  with  the  few 
letters  which  build  up  our  words.  Nor  must  we  forget 
the  extremely  rapid  changes  of  which  the  images  of  sight 
are  capable.  No  wonder,  then,  if  our  senses  speak  to  us 
in  language  which  can  express  far  more  delicate  distinc- 
tions and  richer  varieties  than  can  be  conveyed  by  words. 

This  is  the  solution  of  the  riddle  of  how  it  is  possible 
to  see ;  and,  as  far  as  I  can  judge,  it  is  the  only  one 
of  which  the  facts  at  present  known  admit.  Those 
striking  and  broad  incongruities  between  Sensations  and 
Objects,  both  as  to  quality  and  to  localisation,  on  which 
we  dwelt,  are  just  the  phenomena  which  are  most  in- 
structive ;  because  they  compel  us  to  take  the  right  road. 
And  even  those  physiologists  who  try  to  save  fragments 
of  a  pre-established  harmony  between  sensations  and 
their  objects,  cannot  but  confess  that  the  completion  and 
refinement  of  sensory  perceptions  depend  so  largely  upon 
experience,  that  it  must  be  the  latter  which  finally 
decides  whenever  they  contradict  the  supposed  congenital 
arrangements  of  the  organ.  Hence  the  utmost  signi- 
ficance which  may  still  be  conceded  to  any  such  anatomi- 
cal arrangements  is  that  they  are  possibly  capable  of 
helping  the  first  practice  of  our  senses. 

The  correspondence,  therefore,  between  the  external 
world  and  the  Perceptions  of  Sight  rests,  either  in  whole 
or  in  part,  upon  the  same  foundation  as  all  our  know- 
ledge of  the  actual  world — on  ex'perience^  and  on  constant 
verification  of  its  accuracy  by  experiments  which  we 
perform  with  every  movement  of  our  body.  It  follows, 
of  course,  that  we  are  only  warranted  in  accepting  the 
reality  of  this   correspondence  so  far  as  these  means  of 


816     RECENT   PROGRESS   OF   THE   THEORY   OF   VISION. 

verification  extend,  which  is  really  as  far  as  for  practical 
purposes  we  need. 

Beyond  these  limits,  as,  for  example,  in  the  region  of 
Qualities,  we  are  in  some  instances  able  to  prove  con- 
clusively that  there  is  no  correspondence  at  all  between 
sensations  and  their  objects. 

Only  the  relations  of  time,  of  space,  of  equality,  and 
those  which  are  derived  from  them,  of  number,  size, 
regularity  of  coexistence  and  of  sequence — '  mathematical 
relations'  in  short — are  common  to  the  outer  'and  the 
inner  world,  and  here  we  may  indeed  look  for  a  complete 
correspondence  between  our  conceptions  and  the  objects 
which  excite  them. 

But  it  seems  to  me  that  we  should  not  quarrel  with 
the  bounty  of  nature  because  the  greatness,  and  also  the 
emptiness,  of  these  abstract  relations  have  been  concealed 
from  us  by  the  manifold  brilliance  of  a  system  of  signs  ; 
since  thus  they  can  be  the  more  easily  surveyed  and  used 
for  practical  ends,  while  5^et  traces  enough  remain  visible 
to  guide  the  philosophical  spirit  aright,  in  its  search  after 
the  meaning  of  sensible  Images  and  Signs. 


ON  THE  CONSEEVATION  OF  FOECE. 

INTKODTJCTION   TO   A   SERIES   OF  LECTURES   DELIVERED   AT 
CARLSRUHE  LN   THE  WINTER   OP   1862-1863. 


As  I  have  undertaken  to  deliver  here  a  series  of  lectures, 
I  think  the  best  way  in  which  I  can  discharge  that  duty 
will  be  to  bring  before  you,  by  means  of  a  suitable 
example,  some  view  of  the  special  character  of  thoee 
sciences  to  the  study  of  which  I  have  devoted  myself. 
The  natural  sciences,  partly  in  consequence  of  their 
practical  applications,  and  partly  from  their  intellectual 
influence  on  the  last  four  centuries,  have  so  profoundly, 
and  with  such  increasing  rapidity,  transformed  all  the 
relations  of  the  life  of  civilised  nations ;  they  have 
given  these  nations  such  increase  of  riches,  of  enjoy- 
ment of  life,  of  the  preservation  of  health,  of  means  of 
industrial  and  of  social  intercourse,  and  even  such  in- 
crease of  political  power,  that  every  educated  man  who 
tries  to  understand  the  forces  at  work  in  the  world  in 
which  he  is  living,  even  if  be  does  not  wish  to  enter  upon 
the  study  of  a  special  science,  must  have  some  interest 
in  that  peculiar  kind  of  mental  labour  which  works  and 
acts  in  the  sciences  in  question. 

On  a  former  occasion  I  have  already  discussed  the 
characteristic  differences  which  exist  between  the  natural 
and  the  mental  sciences  as  regards  the  kind  of  scientific 
work.      I   then   endeavoured   to   show   that   it   is   more 


318      ox  THE  COXSERVATIOX  OF  FORCE. 

especially  in  the  thorough  conformity  with  law  which 
natural  phenomena  and  natural  products  exhibit,  and 
in  the  comparative  ease  with  which  laws  can  be  stated, 
that  this  difference  exists.  Not  that  I  wish  by  any  means 
to  deny,  that  the  mental  life  of  individuals  and  peoples 
is  also  in  conformity  with  law,  as  is  the  object  of  philo- 
sophical, philological,  historical,  moral,  and  social  sciences 
to  establish.  But  in  mental  life,  the  influences  are  so 
interwoven,  that  any  definite  sequence  can  but  seldom 
be  demonstrated.  In  Nature  the  converse  is  the  case. 
It  has  been  possible  to  discover  the  law  of  the  origin 
and  progress  of  many  enormously  extended  series  of 
natural  phenomena  with  such  accuracy  and  completeness 
that  we  can  predict  their  future  occurrence  with  the 
gTeatest  certainty;  or  in  cases  in  which  we  have  power 
over  the  conditions  under  which  they  occur,  we  can 
direct  them  just  according  to  our  will.  The  greatest 
of  all  instances  of  what  the  human  mind  can  effect  by 
means  of  a  well-recognised  law  of  natural  phenomena 
is  that  afforded  by  modern  astronomy.  The  one  simple 
law  of  gravitation  regulates  the  motions  of  the  heavenly 
bodies  not  only  of  our  own  planetary  system,  but  also  of 
the  far  more  distant  double  stars ;  from  which,  even  the 
ray  of  light,  the  quickest  of  all  messengers,  needs  years 
to  reach  our  eye ;  and  just  on  account  of  this  simple 
conformity  with  law,  the  motions  of  the  bodies  in  ques- 
tion, can  be  accurately  predicted  and  determined  both 
for  the  past  and  for  futm-e  years  and  centuries  to  a  frac- 
tion of  a  minute. 

On  this  exact  conformity  with  law  depends  also  the 
certainty  with  which  we  know  how  to  tame  the  impetuous 
force  of  steam,  and  to  make  it  the  obedient  servant  of  our 
wants.  On  this  conformity  depends,  moreover,  the  intel- 
lectual fascination  which  chains  the  physicist  to  his  sub- 
jects.    It  is  an  interest  of  quite  a  different  kind  to  that 


ON  THE  CONSERVATION  OF  FORCE.       319 

which  mental  and  moral  sciences  afford.  In  the  latter  it 
is  man  in  the  various  phases  of  his  intellectual  activity 
who  chains  us.  Every  great  deed  of  which  history  tells 
us,  every  mighty  passion  which  art  can  represent,  every 
picture  of  manners,  of  civic  arrangements,  of  the  culture 
of  peoples  of  distant  lands,  or  of  remote  times,  seizes  and 
interests  us,  even  if  there  is  no  exact  scientific  connec- 
tion among  them.  We  continually  find  points  of  contact 
and  comparison  in  our  own  conceptions  and  feelings; 
we  get  to  know  the  hidden  capacities  and  desires  of  the 
mind,  which  in  the  ordinary  peaceful  course  of  civilised 
life  remain  unawakened. 

It  is  not  to  be  denied  that,  in  the  natural  sciences,  this 
kind  of  interest  is  wanting.  Each  individual  fact,  taken 
of  itself,  can  indeed  arouse  our  curiosity  or  our  astonish- 
ment, or  be  useful  to  us  in  its  practical  applications.  But 
intellectual  satisfaction  we  obtain  only  from  a  connection 
of  the  whole,  just  from  its  conformity  with  law.  Reason 
we  call  tliat  faculty  innate  in  us  of  discovering  laws  and 
applying  them  with  thought.  For  the  unfolding  of  the 
peculiar  forces  of  pure  reason  in  their  entire  certainty  and 
in  their  entire  bearing,  there  is  no  more  suitable  arena  than 
inquiry  into  nature  in  the  wider  sense,  the  mathematics 
included.  And  it  is  not  only  the  pleasure  at  the  success- 
ful activity  of  one  of  our  most  essential  mental  powers ; 
and  the  victorious  subjections  to  the  power  of  our  thought 
and  will  of  an  external  world,  partly  unfamiliar,  and  partly 
hostile,  which  is  the  reward  of  this  labour  ;  but  there  is  a 
kind,  I  might  almost  say,  of  artistic  satisfaction,  when  we 
are  able  to  survey  the  enormous  wealth  of  Nature  as  a 
regularly-ordered  whole  —  a  kosmos,  an  image  of  the 
logical  thought  of  our  own  mind. 

The  last  decades  of  scientific  development  have  led  us 
to  the  recognition  of  a  new  universal  law  of  all  natural 
phenomena,  which,  from  its  extraordinarily  extended  range, 


320  ON   THE   CONSEEVATION   OF   FORCE. 

and  from  the  connection  which  it  constitutes  between 
natural  phenomena  of  all  kinds,  even  of  the  remotest 
times  and  the  most  distant  places,  is  especially  fitted  to 
give  us  an  idea  of  what  I  have  described  as  the  character 
of  tlie  natural  sciences,  which  I  have  chosen  as  the  sub- 
ject of  this  lecture. 

This  law  is  the  Laiu  of  the  Conservation  of  Force,  a 
term  the  meaning  of  which  I  must  first  explain.  It  is  not 
absolutely  new ;  for  individual  domains  of  natural  pheno- 
mena it  was  enunciated  by  Newton  and  Daniel  Ber- 
noulli ;  and  Eumford  and  Humphry  Davy  have  recognised 
distinct  features  of  its  presence  in  the  laws  of  heat. 

The  possibility  that  it  was  of  universal  application  was 
first  stated  by  Dr.  Julius  Eobert  Mayer,  a  Schwabian 
pliysician  (now  living  in  Heilbronn)  in  the  year  1842, 
while  almost  simultaneously  with,  and  independently  of 
him,  James  Prescot  Joule,  an  English  manufacturer,  made 
a  series  of  important  and  difficult  experiments  on  the  rela- 
tion of  heat  to  mechanical  force,  which  supplied  the  chief 
points  in  which  the  comparison  of  the  new  theory  with 
experience  was  still  wanting. 

The  law  in  question  asserts,  that  the  quantity  of  force 
luliich  can  be  brought  into  action  in  the  whole  of  Nature 
is  unchangeable,  and  can  neither  be  increased  nor  di- 
minished. JSlj  first  object  will  be  to  explain  to  you  what 
is  understood  by  quantity  of  force  ;  or  as  the  same  idea 
is  more  popularly  expressed  with  reference  to  its  technical 
application,  what  we  call  amount  of  work  in  the  me- 
chanical sense  of  the  word. 

The  idea  of  work  for  machines,  or  natural  processes,  is 
taken  from  comparison  with  the  working  power  of  man ; 
and  we  can  therefore  best  illustrate  from  human  labour, 
the  most  important  features  of  the  question  with  which 
we  are  concerned.  In  speaking  of  the  work  of  machines, 
and  of  natural  forces,  we  must,  of  course,  in  this  compari- 


ON   THE   CONSERVATION   OF   FORCE.  321 

son  eliminate  anything  in  which  activity  of  intelligence, 
comes  into  play.  The  latter  is  also  capable  of  the  hard 
and  intense  work  of  thinking,  which  tries  a  man  just  as 
muscular  exeution  does.  But  whatever  of  the  actions  of 
intelligence  is  met  with  in  the  work  of  machines,  of  course 
is  due  to  the  mind  of  the  constructor  and  cannot  be 
assigned  to  the  instrument  at  work. 

Now,  the  external  work  of  man  is  of  the  most  varied 
kind  as  regards  the  force  or  ease,  the  form  and  rapidity, 
of  the  motions  used  on  it,  and  the  kind  of  work  produced. 
But  both  the  arm  of  the  blacksmith  who  delivers  his 
powerful  blows  with  the  heavy  hammer,  and  that  of  the 
violinist  who  produces  the  most  delicate  variations  in 
sound,  and  the  hand  of  the  lace-maker  who  works  with 
threads  so  fine  that  they  are  on  the  verge  of  the  invisible, 
all  these  acquire  the  force  which  moves  them  in  the  same 
manner  and  by  the  same  organs,  namely,  the  muscles  of 
the  arm.  An  arm  the  muscles  of  which  are  lamed  is  in- 
capable of  doing  any  work  ;  the  moving  force  of  the 
muscle  must  be  at  work  in  it,  and  these  must  obey  the 
nerves,  which  bring  to  them  orders  from  the  brain. 
That  member  is  then  capable  of  the  greatest  variety  of 
motions ;  it  can  compel  the  most  varied  instruments  to 
execute  the  most  diverse  tasks. 

Just  so  is  it  with  machines  :  they  are  used  for  the  most 
diversified  arrangements.  We  produce  by  their  agency 
an  infinite  variety  of  movements,  with  the  most:  various 
degrees  of  force  and  rapidity,  from  powerful  steam- 
hammers  and  rolling-mills,  where  gigantic  masses  of  iron 
are  cut  and  shaped  like  butter,  to  spinning  and  weaving- 
frames,  the  work  of  which  rivals  that  of  the  spider. 
Modern  mechanism  has  the  richest  choice  of  means  of 
transferring  the  motion  of  one  set  of  rolling  wheels  to 
another  with  greater  or  less  velocity  ;  of  changing  the 
rotating  motion  of  wheels  into  the  up-and-down  motion 


322  ON   THE   CONSERVATION   OF   FORCE. 

of  the  piston-rod,  of  the  shuttle,  of  falling  hammers  and 
stamps  ;  or,  conversely,  of  changing  the  latter  into  the 
former;  or  it  can,  on  the  other  hand,  change  move- 
ments of  uniform  into  those  of  varying  velocity,  and  so 
forth.  Hence  this  extraordinarily  rich  utility  of  ma- 
chines for  so  extremely  varied  branches  of  industry.  But 
one  thing  is  common  to  all  these  differences ;  they  all 
need  a  moving  force,  which  sets  and  keeps  them  in 
motion,  just  as  the  works  of  the  human  hand  all  need  the 
moving  force  of  the  muscles. 

Now,  the  work  of  the  smith  requires  a  far  greater  and 
more  intense  exertion  of  the  muscles  than  that  of  the 
violin-player ;  and  there  are  in  machines  corresponding 
differences  in  the  power  and  duration  of  the  moving- 
force  required.  These  differences,  which  correspond  to 
the  different  degree  of  exertion  of  the  muscles  in  human 
labour,  are  alone  what  we  have  to  think  of  when  we 
speak  of  the  amount  of  ivork  of  a  machine.  We  have 
nothing  to  do  here  with  the  manifold  character  of  the 
actions  and  arrangements  which  the  machines  produce ; 
we  are  only  concerned  with  an  expenditure  of  force. 

This  very  expression  which  we  use  so  fluently,  '  expen- 
diture of  force,'  which  indicates  that  the  force  applied 
has  been  expended  and  lost,  leads  us  to  a  further  charac- 
teristic analogy  between  the  effects  of  the  human  arm  and 
those  of  machines.  The  greater  the  exertion,  and  the 
longer  it  lasts,  the  more  is  the  arm  tired,  and  the  more 
is  the  store  of  its  moving  force  for  the  time  exhausted. 
We  shall  see  that  this  peculiarity  of  becoming  exhausted 
by  work  is  also  met  with  in  the  moving  forces  of  inor- 
jjanic  nature  ;  indeed,  that  this  capacity  of  the  human 
arm  of  being  tired  is  only  one  of  the  consequences  of  the 
law  with  which  we  are  now  concerned.  When  fatigue 
sets  in,  recovery  is  needed,  and  this  can  only  be  effected 
by  rest  and  nourishment.     We  shall  find  that  also  in  the 


ox   THE   CONSERVATION   OF   FORCE.  323 

inorganic  moving  forces,  when  their  capacity  for  work  is 
spent,  there  is  a  possibility  of  reproduction,  although  in 
general  other  means  must  be  used  to  this  end  than  in  the 
case  of  the  human  arm. 

From  the  feeling  of  exertion  and  fatigue  in  our  muscles, 
we  can  form  a  general  idea  of  what  we  understand  by 
amount  of  work  ;  but  we  must  endeavour,  instead  of  the 
indefinite  estimate  afforded  by  this  comparison,  to  form  a 
clear  and  precise  idea  of  the  standard  by  which  we  have 
to  measure  the  amount  of  work.  This  we  can  do  better 
by  the  simplest  inorganic  moving  forces  than  by  the 
actions  of  our  muscles,  which  are  a  very  complicated 
apparatus,  acting  in  an  extremely  intricate  manner. 

Let  us  now  consider  that  moving  force  which  we  know 
best,  and  which  is  simplest — gravity.  It  acts,  for  ex- 
ample as  such,  in  those  clocks  which  are  driven  by  a 
weight.  This  weight  fastened  to  a  string,  which  is  wound 
round  a  pulley  connected  with  the  first  toothed  wheel  of 
the  clock,  cannot  obey  the  pull  of  gravity  without  setting 
the  whole  clockwork  in  motion.  Now  I  must  beg  you  to 
pay  special  attention  to  the  following  points  :  the  weight 
cannot  put  the  clock  in  motion  without  itself  sinking ; 
did  the  weight  not  move,  it  could  not  move  the  clock, 
and  its  motion  can  only  be  such  a  one  as  obeys  the  action 
of  gravity.  Hence,  if  the  clock  is  to  go,  the  weight  must 
continually  sink  lower  and  lower,  and  must  at  length  sink 
so  far  that  the  string  which  supports  it  is  run  out.  The 
clock  then  stops.  The  useful  effect  of  its  weight  is  for  the 
present  exhausted.  Its  gravity  is  not  lost  or  diminished  ; 
it  is  attracted  by  the  earth  as  before,  but  the  capacity  of 
this  gravity  to  produce  the  motion  of  the  clockwork  is  lost. 
It  can  only  keep  the  weight  at  rest  in  the  lowest  point  of 
its  path,  it  cannot  farther  put  it  in  motion. 

But  we  can  wind  up  the  clock  by  the  power  of  the  arm, 
by  which  the  weight  is  again  raised.  When  this  has  been 
15 


324       ON  THE  CONSEEVATION  OF  FORCE. 

done,  it  has  regained  its  former  capacity,  and  can  again 
set  the  clock  in  motion. 

We  learn  from  this  that  a  raised  weight  possesses  a 
TYioving  force^  but  that  it  must  necessarily  sink  if  this 
force  is  to  act ;  that  by  sinking,  this  moving  force  is 
exhausted,  but  by  using  another  extraneous  moving  force 
-^that  of  the  arm — its  activity  can  be  restored. 

The  work  which  the  weight  has  to  perform  in  driving 
the  clock  is  not  indeed  great.  It  has  continually  to 
overcome  the  small  resistances  which  the  friction  of  the 
axles  and  teeth,  as  well  as  the  resistance  of  the  air,  oppose 
to  the  motion  of  the  wheels,  and  it  has  to  furnish  the 
force  for  the  small  impulses  and  sounds  which  the 
pendulum  produces  at  each  oscillation.  If  the  weight  is 
detached  from  the  clock,  the  pendulum  swings  for  a 
while  before  coming  to  rest,  but  its  motion  becomes  each 
moment  feebler,  and  ultimately  ceases  entirely,  being 
gradually  used  up  by  the  small  hindrances  I  have  men- 
tioned. Hence,  to  keep  the  clock  going,  there  must  be  a 
moving  force,  which,  though  small,  must  be  continually 
at  work.     Such  a  one  is  the  weight. 

We  get,  moreover,  from  this  example,  a  measure  for  the 
amount  of  work.  Let  us  assume  that  a  clock  is  driven 
by  a  weight  of  a  pound,  which  falls  five  feet  in  twenty- 
four  hours.  If  we  fix  ten  such  clocks,  each  with  a  weiglit 
of  one  pound,  then  ten  clocks  will  be  driven  twenty- four 
hours  ;  hence,  as  each  has  to  overcome  the  same  resistances 
in  the  same  time  as  the  others,  ten  times  as  much  work 
is  performed  for  ten  pounds  fall  through  five  feet.  Hence, 
we  conclude  that  the  height  of  the  fall  being  the  same, 
the  work  increases  directly  as  the  weiglit. 

Now,  if  we  increase  the  length  of  the  string  so  that 
the  weight  runs  down  ten  feet,  the  clock  will  go  two 
days  instead  of  one ;  and,  with  double  the  height  of  fall, 
the   weight  will  overcome   on  the  second  day  the  same 


ON   THE    CONSERVATION    OF    FORCE.  325 

resistances  as  on  the  first,  and  will  therefore  do  twice  as 
much  work  as  when  it  can  only  run  down  five  feet.  The 
weight  being  the  same,  the  work  increases  as  the  height 
of  fall.  Hence,  we  may  take  the  product  of  the  weight 
into  the  height  of  fall  as  a  measure  of  work,  at  any  rate, 
in  the  present  case.  The  application  of  this  measure  is, 
in  fact,  not  limited  to  the  individual  case,  but  the  uni- 
versal standard  adopted  in  manufactures  for  measuring 
magnitude  of  work  is  'a.  foot  'pound — that  is,  the  amount 
of  work  which  a  pound  raised  through  a  foot  can  produce.^ 

We  may  apply  this  measure  of  work  to  all  kinds  of 
machines,  for  we  should  be  able  to  set  them  all  in 
motion  by  means  of  a  weight  sufficient  to  turn  a  pulley. 
We  could  thus  always  express  the  magnitude  of  any 
driving  force,  for  any  given  machine,  by  the  magnitude 
and  height  of  fall  of  such  a  weight  as  would  be  necessary 
to  keep  the  machine  going  with  its  arrangements  until  it 
had  performed  a  certain  work.  Hence  it  is  that  the 
measurement  of  work  by  foot  pounds  is  universally  ap- 
plicable. The  use  of  such  a  weight  as  a  driving  force 
would  not  indeed  be  practically  advantageous  in  those 
cases  in  which  we  were  compelled  to  raise  it  by  the  power 
of  our  own  arm ;  it  would  in  that  case  be  simpler  to  work 
the  machine  by  the  direct  action  of  the  arm.  In  the 
clock  we  use  a  weight  so  that  we  need  not  stand  the  whole 
day  at  the  clockwork,  as  we  should  have  to  do  to  move  it 
directly.  By  winding  up  the  clock  we  accumulate  a  store 
of  working  capacity  in  it,  which  is  sufficient  for  the  ex- 
penditure of  the  next  twenty-foiu:  hours. 

The  case  is  somewhat  different  when  Nature  herself 
raises  the  weight,  which  then  works  for  us.  She  does  not 
do  this  with  solid  bodies,  at  least  not  with  such  regularity 
as  to  be  utilised ;  but  slie  does  it  abundantly  with  water, 

>  This  is  the  technical  measure  of  -work;   to  convert  it  into  scientific 
measure  it  must  be  multiplied  by  the  intensity  of  gravity. 


326 


ON   THE   COXSERVATION   OF    FORCE. 


which,  being  raised  to  the  tops  of  mountains  by  meteoro- 
logical processes,  returns  in  streams  from  them.  The 
gravity  of  water  we  use  as  moving  force,  the  most  direct 
application  being  in  what  are  called  overshot  wheels,  one 
of  which  is  represented  in  Fig.  38.  Along  the  circumfer- 
ence of  such  a  wheel  are  a  series  of  buckets,  which  act  as 


Fig.  38. 


receptacles  for  the  water,  and,  on  the  side  turned  to  the 
observer,  have  the  tops  uppermost ,  on  the  opposite  side 
the  tops  of  the  buckets  are  upside-down.  The  water  flows 
at  M  into  the  buckets  of  the  front  of  the  wheel,  and  at 
P',  %vhere  the  mouth  begins  to  incline  downwards,  it  flows 
out.     The  buckets  on  the  circumference  are  filled  on  the 


ON  THE  CONSERVATION  OF  FORCE.       327 

side  turned  to  the  observer,  and  empty  on  the  other  side. 
Thus  the  former  are  weighted  by  the  water  contained  in 
them,  the  latter  not ;  the  weight  of  the  water  acts  con- 
tinuously on  only  one  side  of  the  wheel,  draws  this  down, 
and  thereby  turns  the  wheel ;  the  other  side  of  the  wheel 
offers  no  resistance,  for  it  contains  no  water.  It  is  thus 
the  weight  of  the  falling  water  which  tm'ns  the  wheel, 
and  furnishes  the  motive  power.  But  you  will  at  once  see 
that  the  mass  of  water  which  turns  the  wheel  must  neces- 
sarily fall  in  order  to  do  so,  and  that  though,  when  it 
has  reached  the  bottom,  it  has  lost  none  of  its  gravity,  it 
is  no  longer  in  a  position  to  drive  the  Avheel,  if  it  is  not 
restored  to  its  original  position,  either  by  the  power  of 
the  human  arm  or  by  means  of  some  other  natural  force. 
If  it  can  flow  from  the  mill-stream  to  still  lower  levels, 
it  may  be  used  to  work  other  wheels.  But  when  it  has 
reached  its  lowest  level,  the  sea,  the  last  remainder  of 
the  moving  force  is  used  up,  which  is  due  to  gravity — 
that  is,  to  the  attraction  of  the  earth,  and  it  cannot  act 
by  its  weight  until  it  has  been  again  raised  to  a  high  level. 
As  this  is  actually  effected  by  meteorological  processes, 
you  will  at  once  observe  that  these  are  to  be  considered  as 
sources  of  moving  force. 

Water-power  was  the  first  inorganic  force  which  man 
learnt  to  use  instead  of  his  own  labour  or  of  that  of  domes- 
tic animals.  According  to  Strabo,  it  was  known  to  King 
Mithridates,  of  Pontus,  who  was  also  otherwise  celebrated 
for  his  knowledge  of  nature  ;  near  his  palace  there  was  a 
water-wheel.  Its  use  was  first  introduced  among  the 
Eomans  in  the  time  of  the  first  Emperors.  Even  now  we 
find  water-mills  in  all  mountains,  valleys,  or  wherever 
there  are  rapidly-flowing,  regularly-filled,  brooks  and 
streams.  We  find  water-power  used  for  all  purposes  which 
can  possibly  be  effected  by  machines.  It  drives  mills 
which  grind   corn,   saw-mills,   hammers   and  oil-presses, 


328  ox   THE   CONSERVATION   OF   FORCE. 

spinning-frames  and  looms,  and  so  forth.  It  is  the 
cheapest  of  all  motive  powers,  it  flows  spontaneously 
from  the  inexhaustible  stores  of  nature  ;  but  it  is  re- 
stricted to  a  particular  place,  and  only  in  mountainous 
countries  is  it  present  in  any  quantity ;  in  level  countries 
extensive  reservoirs  are  necessary  for  damming  the  rivers 
to  produce  any  amount  of  water-power. 

Before  passing  to  the  discussion  of  other  motive  forces, 
I  must  answer  an  objection  which  may  readily  suggest 
itself.  We  all  know  that  there  are  numerous  machines, 
systems  of  pulleys,  levers  and  cranes,  by  the  aid  of  which 
heavy  burdens  may  be  lifted  by  a  comparatively  small 
expenditure  of  force.  We  have  all  of  us  often  seen  one  or 
two  workmen  hoist  heavy  masses  of  stones  to  great  heights, 
which  they  would  be  quite  unable  to  do  directly  ;  in  like 
manner,  one  or  two  men,  by  means  of  a  crane,  can  trans- 
fer the  largest  and  heaviest  chests  from  a  ship  to  the  quay. 
Now  it  may  be  asked,  If  a  large,  heavy  weight  had  been 
used  for  driving  a  machine,  would  it  not  be  very  easy,  by 
means  of  a  crane  or  a  system  of  pulleys,  to  raise  it  anew, 
so  that  it  could  again  be  used  as  a  motor,  and  thus  acquire 
motive  power,  without  being  compelled  to  use  a  corre- 
sponding exertion  in  raising  the  weight  ? 

The  answer  to  this  is,  that  all  these  machines,  in  that 
degree  in  which  for  the  moment  they  facilitate  the  exer- 
tion, also  prolong  it,  so  that  by  their  help  no  motive  power 
is  ultimately  gained.  Let  us  assume  that  four  labourers 
have  to  raise  a  load  of  four  hundredweight,  by  means  of 
a  rope  passing  over  a  single  pulley.  Every  time  the  rope 
is  pulled  down  through  four  feet,  the  load  is  also  raised 
through  four  feet.  But  now,  for  the  sake  of  comparison, 
let  us  suppose  the  same  load  hung  to  a  block  of  four 
pulleys,  as  represented  in  Fig.  39.  A  single  labourer 
would  now  be  able  to  raise  the  load  by  the  same  exertion 
of  force  as  each  one  of  the  four  put  forth.     But  when  he 


ON   THE    CONSERVATION    OF    FORCE. 


329 


Fio.  39. 


pulls  the  rope  throiigli  four  feet,  the  load  only  rises  one 

foot,  for  the  length  through  which  he  pulls  the  rope,  at  a,  is 

uniformly  distributed  in  the  block  over  four  ropes,  so  that 

each  of  these  is  only  shortened 

by   a  foot.     To    raise    the  load, 

therefore,   to    the    same    height, 

the    one   man    must   necessarily 

work  four  times  as  long  as  the 

four  together  did.     But  the  total 

expenditure  of  work  is  the  same, 

whether  four  labourers  work  for 

a  quarter  of  an  hour  or  one  works 

for  an  hour. 

If,  instead  of  human  labour, 
we  introduce  the  work  of  a 
weight,  and  hang  to  the  block  a 
load  of  400,  and  at  a,  where 
otherwise  the  labourer  works,  a 
weight  of  100  pounds,  the  block 
is  then  in  equilibrium,  and, 
without  any  appreciable  exer- 
tion of  the  arm,  may  be  set  in 
motion.  The  weight  of  100 
pounds  sinks,  that  of  400  rises. 
Without  any  measurable  expen- 
diture of  force,  the  heavy  weight 
has  been  raised  by  the  sinking 
of  the  smaller  one.  But  observe 
that  the  smaller  weight  will 
have  sunk  through  four  times 
the    distance    that    the    greater 

one  has  risen.  But  a  fall  of  100  pounds  through  four 
feet  is  just  as  much  400  foot  pounds  as  a  fall  of  400  pounds 
through  one  foot. 

The  action  of  levers  in  all  their  various  modifications 


330  ON   THE   CONSERVATION   OF   FORCE. 

is  precisely  similar.  Let  a  b.  Fig.  40,  be  a  simple  lever, 
supported  at  c,  the  arm  c  b  being  four  times  as  long  as  the 
other  arm  a  c.  Let  a  weight  of  one  pound  be  hung  at  6, 
and  a  weight  of  four  pounds  at  a,  the  lever  is  then  in  equi- 
librium, and  the  least  pressure  of  the  finger  is  sufficient, 
without  any  appreciable  exertion  of  force,  to  place  it  in 
the  position  a'  b\  in  which  the  heavy  weight  of  four 
pounds  has  been  raised,  while  the  one-pound  weight  has 
sunk.  But  here,  also,  you  will  observe  no  work  has 
been  gained,  for  while  the  heavy  weight  has  been  raised 

Fig.  40. 


through  one  inch,  the  lighter  one  has  fallen  through 
four  inches  ;  and  four  pounds  through  one  inch  is,  as  work, 
equivalent  to  the  product  of  one  pound  through  four 
inches. 

Most  other  fixed  parts  of  machines  may  be  regarded  as 
modified  and  compound  levers ;  a  toothed-wheel,  for  in- 
stance as  a  series  of  levers,  the  ends  of  which  are  repre- 
sented by  the  individual  teeth,  and  one  after  the  other  of 
which  is  put  in  activity,  in  the  degree  in  which  the 
tooth  in  question  seizes,  or  is  seized  by  the  adjacent 
pinion.  Take,  for  instance,  the  crabwinch,  represented  in 
Fig.  41.     Suppose  the  pinion  on  the  axis  of  the  barrel  of 


ON  THE   CONSERVATION   OP   FORCE. 


831 


the  winch  has  twelve  teeth,  and  the  toothed-wheel,  H  H, 
seventy-two  teeth,  that  is  six  times  as  many  as  the 
former.  The  winch  must  now  be  tm-ned  round  six  times 
before  the  toothed-wheel,  H,  and  the  barrel,  D,  have 
made  one  turn,  and  before  the  rope  which  raises  the  load 
has  been  lifted  by  a  length  equal  to  the  circumference  of 
the  barrel.     The  workman   thus  requires  six  times  the 

Fig.  41. 


time,  though  to  be  sure  only  one-sixth  of  the  exertion, 
which  he  would  have  to  use  if  the  handle  were  directly 
applied  to  the  barrel,  D.  In  all  these  machines,  and  parts 
of  machines,  we  find  it  confirmed  that  in  proportion  as 
the  velocity  of  the  motion  increases  its  power  diminishes, 
and  that  wlien  the  power  increases  tlie  velocity  diminishes, 
but  that  the  amount  of  work  is  never  thereby  increased. 

In  the  overshot  mill-wheel,  described  above,  water  acts 
by  its  weight.     But  there  is  another  form  of  mill-wheels, 


332 


ON  THE  CONSERVATION   OP   FORCE. 


what  is  called  the  undershot  wheels  in  which  it  only  acts 
by  its  impact,  as  represented  in  Fig.  42.  These  are  used 
where  the  height  from  which  the  water  comes  is  not  great 
enough  to  flow  on  the  upper  part  of  the  wheel.  The 
lower  part  of  undershot  wheels  dips  in  the  flowing  water 
which  strikes  against  their  float-boards  and  carries  them 
along.  Such  wheels  are  used  in  swift-flowing  streams 
which  have  a  scarcely  perceptible  fall,  as,  for  instancej  on 

Fig.  42. 


the  Ehine.  In  the  immediate  neighbourhood  of  such  a 
wheel,  the  water  need  not  necessarily  have  a  great  fall  if 
it  only  strikes  with  considerable  velocity.  It  is  the  velo- 
city of  tlie  water,  exerting  an  impact  against  the  float- 
boards,  which  acts  in  this  case,  and  which  produces  the 
motive  power. 

Windmills,  which  are  used  in  the  great  plains  of  Holland 
and  North  Grermaiiy  to  supply  the  want  of  falling  water, 
aft'ord  another  instance  of  the  action  of  velocity.     The 


ON  THE  CONSERVATION  OF  FORCE.       333 

sails  are  driven  by  air  in  motion — by  wind.  Air  at  rest 
could  just  as  little  drive  a  windmill  as  water  at  rest  a 
water-wheel.  The  driving  force  depends  here  on  the 
velocity  of  moving  masses. 

A  bullet  resting  in  the  hand  is  the  most  harmless  thing 
in  the  world  ;  by  its  gravity  it  can  exert  no  great  effect ; 
but  when  fired  and  endowed  with  great  velocity  it  drives 
through  all  obstacles  with  the  most  tremendous  force. 

If  I  lay  the  head  of  a  hammer  gently  on  a  nail,  neither 
its  small  weight  nor  the  pressure  of  my  arm  is  quite 
sufficient  to  drive  the  nail  into  wood  ;  but  if  I  swing  the 
hammer  and  allow  it  to  fall  with  great  velocity,  it 
acquires  a  new  force,  which  can  overcome  far  greater 
hindrances. 

These  examples  teach  us  that  the  velocity  of  a  moving- 
mass  can  act  as  motive  force.  In  mechanics,  velocity  in 
so  far  as  it  is  motive  force,  and  can  produce  work,  is 
called  vis  viva.  The  name  is  not  well  chosen  ;  it  is  too 
apt  to  suggest  to  us  the  force  of  living  beings.  Also  in 
this  case  you  will  see,  f*'om  the  instances  of  the  hammer 
and  of  the  bullet,  that  velocity  is  lost  as  such,  when  it 
produces  working  power.  In  the  case  of  the  water-mill, 
or  of  the  windmill,  a  more  careful  investigation  of  the 
moving  masses  of  water  and  air  is  necessary  to  prove  that 
part  of  their  velocity  has  been  lost  by  the  work  which 
they  have  performed. 

The  relation  of  velocity  to  working  power  is  most 
simply  and  clearly  seen  in  a  simple  pendulum,  such  as  can 
be  constructed  by  any  weight  which  we  suspend  to  a  cord. 
Let  M,  Fig.  43,  be  such  a  weight,  of  a  spherical  form  ;  A  B, 
a  horizontal  line  drawn  through  the  centre  of  the  sphere ; 
P  the  point  at  which  the  cord  is  fastened.  If  now  I  draw 
the  weight  M  on  one  side  towards  A,  it  moves  in  the  arc 
M  a,  the  end  of  which,  a,  is  somewhat  higher  than  the 
point  A  in  the  horizontal  line.     The  weight  is  thereby 


334 


ON   THE   COXSERYATION   OF   FORCE. 


raised  to  the  height  A  a.  Hence  my  arm  must  oxert  a 
certain  force  to  bring  the  weight  to  a.  Gravity  resists 
this  motion  and  endeavours  to  bring  back  the  weight  to 
M,  the  lowest  point  which  it  can  reach. 

Now,  if  after  I  have  brought  the  weight  to  a  I  let  it 
go,  it  obeys  this  force  of  gravity  and  returns  to  M,  arrives 
there  with  a  certain  velocity,  and  no  longer  remains 
quietly  hanging  at  M  as  it  did  before,  but  savings  be- 

FiG.  43. 


yond  M  towards  6,  where  its  motion  stops  as  soon  as  it 
has  traversed  on  the  side  of  B  an  arc  equal  in  length  to 
that  on  the  side  of  A,  and  after  it  has  risen  to  a  distance 
B  b  above  the  horizontal  line,  which  is  equal  to  the  height 
A  a,  to  which  my  arm  had  previously  raised  it.  In  b  the 
pendulum  returns,  swings  the  same  way  back  through  M 
towards  a,  and  so  on,  until  its  oscillations  are  gradually 
diminished,  and  ultimately  annulled  by  the  resistance  of 
the  air  and  by  friction. 


ON   THE   CONSERVATION   OF   FORCE.  335 

You  see  here  that  the  reason  why  the  weight,  when  it 
comes  from  a  to  M,  and  does  not  stop  there,  but  ascends 
to  6,  in  opposition  to  the  action  of  gravity,  is  only  to  be 
sought  in  its  velocity.  The  velocity  which  it  has  ac- 
quired in  moving  from  the  height  A  a  is  capable  of  again 
^raising  it  to  an  equal  height,  B  h.  The  velocity  of  the 
moving  mass,  M,  is  thus  capable  of  raising  this  mass  ; 
that  is  to  say,  in  the  language  of  mechanics,  of  performing 
work.  This  would  also  be  the  case  if  we  had  imparted 
such  a  velocity  to  the  suspended  weight  by  a  blow. 

From  this  we  learn  further  how  to  measure  the  workin  g 
power  of  velocity — or,  what  is  the  same  thing,  the  vis 
viva  of  the  moving  mass.  It  is  equal  to  the  work, 
expressed  in  foot  pounds,  which  the  same  mass  can 
exert  after  its  velocity  has  been  used  to  raise  it,  under 
the  most  favourable  circumstances,  to  as  great  a  height 
as  possible.^  This  does  not  depend  on  the  direction  of 
the  velocity ;  for  if  we  swing  a  weight  attached  to  a 
thread  in  a  circle,  we  can  even  change  a  downward 
motion  into  an  upward  one. 

The  motion  of  the  pendulum  shows  us  very  distinctly 
how  the  forms  of  working  power  hitherto  considered — 
that  of  a  raised  weight  and  that  of  a  moving  mass — may 
merge  into  one  another.  In  the  points  a  and  6,  Fig.  43, 
the  mass  has  no  velocity ;  at  the  point  M  it  has  fallen  as 
far  as  possible,  but  possesses  velocity.  As  the  weight  goes 
from  a  to  m  the  work  of  the  raised  weight  is  changed  into 
vis  viva;  as  the  weight  goes  further  from  m  to  6  the  vis 
viva  is  changed  into  the  work  of  a  raised  weight.  Thus  the 
work  which  the  arm  originally  imparted  to  the  pendulum 
is  not  lost  in  these  oscillations,  provided  we  may  leave  out 
of  consideration  the  influence  of  the  resistance  of  the  air 

'  The  measure  of  vis  viva  in  theoretical  mechanics  is  half  the  product  of 
the  weight  into  the  square  of  the  velocity.  To  reduce  it  to  the  technical 
measure  of  the  work  we  must  divide  it  by  the  intensity  of  gravity  ;  that 
is,  by  the  velocity  at  the  end  of  the  first  second  of  a  freely  falling  body. 


336      ON  THE  CONSERVATION  OF  FORCE. 

and  of  friction.  Neither  does  it  increase,  but  it  continually 
changes  the  form  of  its  manifestation. 

Let  us  now  pass  to  other  mechanical  forces,  those 
of  elastic  bodies.  Instead  of  the  weights  which  drive 
our  clocks,  we  find  in  time-pieces  and  in  watches,  steel 
springs  which  are  coiled  in  winding  up  the  clock,  and 
are  uncoiled  by  the  working  of  the  clock.  To  coil  up  the 
spring  we  consume  the  force  of  the  arm  ;  this  has  to 
overcome  the  resisting  elastic  force  of  the  spring  as  we 
wind  it  up,  just  as  in  the  clock  we  have  to  overcome  the 
force  of  gravity  which  the  weight  exerts.  The  coiled 
spring  can,  however,  perform  work  ;  it  gradually  expends 
this  acquired  capability  in  driving  the  clockwork. 

If  I  stretch  a  crossbow  and  afterwards  let  it  go,  the 
stretched  string  moves  the  arrow  ;  it  imparts  to  it  force 
in  the  form  of  velocity.  To  stretch  the  cord  my  arm 
must  work  for  a  few  seconds ;  this  work  is  imparted 
to  the  arrow  at  the  moment  it  is  shot  off.  Thus  the 
crossbow  concentrates  into  an  extremely  short  time 
the  entire  work  which  the  arm  had  communicated  in  the 
operation  of  stretching;  the  clock,  on  the  contrary, 
spreads  it  over  one  or  several  days.  In  both  cases  no 
work  is  produced  which  my  arm  did  not  originally  impart 
to  the  instrument,  it  is  only  expended  more  conveniently. 

The  case  is  somewhat  different  if  by  any  other  natural 
process  I  can  place  an  elastic  body  in  a  state  of  tension 
witliout  having  to  exert  my  arm.  This  is  possible  and 
is  most  easily  observed  in  the  case  of  gases. 

If,  for  instance,  I  discharge  a  fire-arm  loaded  ^^ith 
gunpowder,  the  greater  part  of  the  mass  of  the  powder  is 
converted  into  gases  at  a  very  high  temperature,  which 
have  a  powerful  tendency  to  expand,  and  can  only  be 
retained  in  the  narrow  space  in  which  they  are  formed, 
by  the  exercise  of  the  most  powerful  pressure.  In 
expanding  with  enormous  force  they  propel  the  bullet, 


ON   THE   CONSERVATION   OF   FORCE. 


337 


and  impart  to  it  a  great  velocity,  which  we  have  already 
seen  is  a  form  of  work. 

In  this  case,  then,  I  have  gained  work  which  my  arm 
has  not  performed.  Something,  however,  has  been  lost  ; 
the  gunpowder,  that  is  to  say,  whose  constituents  have 
changed  into  other  chemical  compounds,  from  which 
they  cannot,  without  further  ado,  be  restored  to  their 
original  condition.  Here,  then,  a  chemical  change  has 
taken  place,  under  the  influence  of  which  work  has  been 
gained. 

Elastic  forces  are  produced  in  gases  by  the  aid  of  heat, 
on  a  far  greater  scale. 

Let  us  take,  as  the  most  simple  instance,  atmospheric 
air.     In   Fig.  44  an   apparatus   is   represented  such   as 

Fig.  44. 


Regnault  used  for  measuring  the  expansive  force  of  heated 
gases.     If  no  great  accuracy  is  required  in  the  measure- 


338  ox  THE   CONSERVATION   OF   FORCE. 

ment,  the  apparatus  may  be  arranged  more  simply.  At 
C  is  a  glass  globe  filled  with  dry  air,  which  is  placed  in 
a  metal  vessel,  in  which  it  can  be  heated  by  steam.  It  is 
connected  with  the  U-shaped  tube,  s  s,  which  contains  a 
liquid,  and  the  limbs  of  which  communicate  with  each 
other  when  the  stop-cock  r  is  closed.  If  the  liquid  is  in 
equilibrium  in  the  tube  ss  when  the  globe  is  cold,  it 
rises  in  the  leg  s,  and  ultimately  overflows  when  the 
globe  is  heated.  If,  on  the  contrary,  when  the  globe  is 
heated,  equilibrium  be  restored  by  allowing  some  of  the 
liquid  to  flow  out  at  R,  as  the  globe  cools  it  will  be  drawn 
up  towards  n.  In  both  cases  liquid  is  raised,  and  work 
thereby  produced. 

The  same  experiment  is  continuously  repeated  on  the 
largest  scale  in  steam  engines,  though  in  order  to  keep 
up  a  continual  disengagement  of  compressed  gases  from 
the  boiler,  the  air  in  the  globe  in  Fig.  44,  which  would 
soon  reach  the  maximum  of  its  expansion,  is  replaced  by 
water,  w^hich  is  gradually  changed  into  steam  by  the 
application  of  heat.  But  steam,  so  long  as  it  remains 
as  such,  is  an  elastic  gas  which  endeavours  to  expand 
exactly  like  atmospheric  air.  And  instead  of  the  column 
of  liquid  which  was  raised  in  our  last  experiment,  the 
machine  is  caused  to  drive  a  solid  piston  which  imparts 
its  motion  to  other  parts  of  the  machine.  Fig.  45  re- 
presents a  front  view  of  the  working  parts  of  a  high 
pressure  engine,  and  Fig.  46  a  section.  The  boiler  in 
which  steam  is  generated  is  not  represented  ;  the  steam 
passes  through  the  tube  z  z,  F'ig.  46,  to  the  cylinder  a  a, 
in  which  moves  a  tightly  fitting  piston  c.  The  parts 
between  the  tube  z  z  and  the  cylinder  a  a,  that  is  the 
slide  valve  in  the  valve-chest  K  k,  and  the  two  tubes  d 
and  e  allow  the  steam  to  pass  first  below  and  then  above 
the  piston,  while  at  the  same  time  the  steam  has  free 
exit  from   the    other    half  of  the  cylinder.     When  the 


ON   THE   CONSERVATION   OF   FORCE. 

Ficr.  45. 


339 


340      ON   THE  CONSERVATION  OF  FORCE. 

Fig.  46. 


Oy   THE    CONSERVATION    OF   FORCE.  341 

steam  passes  under  the  piston,  it  forces  it  upward  ;  when 
the  piston  has  rear'-hed  the  top  of  its  course  the  position 
of  the  valve  in  k  k  changes,  and  the  steam  passes  above 
the  piston  and  forces  it  down  again.  The  piston-rod  acts 
by  means  of  the  connecting-rod  p,  on  the  crank  Q  of  the 
fly-wheel  x  and  sets  tliis  in  motion.  By  means  of  the 
rod  s,  the  motion  of  the  rod  regulates  the  opening  and 
closing  of  the  valve.  But  we  need  not  here  enter  into 
those  mechanical  arrangements,  however  ingeniously  they 
have  been  devised.  We  are  only  interested  in  the  manner 
in  which  heat  produces  elastic  vapour,  and  how  this 
vapour,  in  its  endeavour  to  expand,  is  compelled  to  move 
the  solid  parts  of  the  machine,  and  furnish  work. 

You  all  know  how  powerful  and  varied  are  the  effects 
of  which  steam  engines  are  capable ;  with  them  has 
really  begun  the  great  development  of  industry  which 
has  characterised  our  century  before  all  others.  Its 
most  essential  superiority  over  motive  powers  formerly 
known,  is  that  it  is  not  restricted  to  a  particular  place. 
Tlie  store  of  coal  and  the  small  quantity  of  water 
which  are  the  sources  of  its  power  can  be  brought 
everywhere,  and  steam  engines  can  even  be  made  mov- 
able, as  is  the  case  with  steam-ships  and  locomotives. 
By  means  of  these  machines  we  can  develope  motive 
power  to  almost  an  indefinii)e  extent  at  any  place  on  the 
earth's  surface,  in  deep  mines  and  even  on  the  middle 
of  the  ocean  ;  while  water  and  wind-mills  are  bound  to 
special  parts  of  the  surface  of  the  land.  The  locomotive 
transports  travellers  and  goods  over  the  land  in  numbers 
and  with  a  speed  which  must  have  seemed  an  incredible 
fable  to  our  forefathers,  who  looked  upon  the  mail- 
coach  with  its  six  passengers  in  the  inside  and  its  ten 
miles  an  hour,  as  an  enormous  progress.  Steam-engines 
traverse  the  ocean  independently  of  the  direction  of  the 
wind,  and,  successfully  resisting  storms  which  would  drive 


342  01^   THE   CONSERVATION   OF   FORCE. 

sailing-vessels  far  away,  reach  their  goal  at  the  appointed 
time.  The  advantages  which  the  concourse  of  numerous, 
and  variously  skilled  workmen  in  all  branches  offers  in 
large  towns  where  wind  and  water  power  are  wanting,  can 
be  utilised,  for  steam-engines  find  place  everywhere, 
and  supply  the  necessary  crude  force  ;  thus  the  more  in- 
telligent human  force  may  be  spared  for  better  purposes ; 
and,  indeed,  wherever  the  nature  of  the  ground  or  the 
neighbourhood  of  suitable  lines  of  communication  present 
a  favourable  opportunity  for  the  development  of  industry, 
the  motive  power  is  also  present  in  the  form  of  steam- 
engines. 

We  see,  then,  that  heat  can  produce  mechanical  power ; 
but  in  the  cases  which  we  have  discussed  we  have  seen 
that  the  quantity  of  farce  which  can  be  produced  by  a 
given  measure  of  a  physical  process  is  always  accurately 
defined,  and  that  the  further  capacity  for  work  of  the 
natural  forces,  is  either  diminished  or  exhausted  by  the 
work  which  has  been  performed.  How  is  it  now  with  Heat 
in  this  respect  ? 

This  question  was  of  decisive  importance  in  the  en- 
deavour to  extend  the  law  of  the  Conservation  of  Force 
to  all  natural  processes.  In  the  answer  lay  the  chief 
difference  between  the  older  and  newer  views  in  these 
respects.  Hence  it  is  that  many  physicists  designate 
that  view  of  Nature  corresponding  to  the  law  of  the 
conservation  of  force  with  the  name  of  the  Mechanical 
Theoi^  of  Heat. 

The  older  view  of  the  nature  of  heat  was  that  it  is  a 
substance,  very  fine  and  imponderable  indeed,  but  in- 
destructible, and  unchangeable  in  quantity,  which  is  an 
essential  fundamental  property  of  all  matter.  And,  in 
fact,  in  a  large  number  of  natural  processes,  the  quantity 
of  heat  which  can  be  demonstrated  by  the  thermometer 
is  unchangeable. 


ON   THE   CONSERVATION   OF   FORCE.  343 

By  conduction  and  radiation,  it  can  indeed  pass  from 
hotter  to  colder  bodies  ;  but  the  quantity  of  heat  which 
tlie  former  lose  can  be  shown  by  the  thermometer  to  have 
reappeared  in  the  latter.  Many  processes,  too,  were 
known,  especially  in  the  passage  of  bodies  from  the  solid 
to  the  liquid  and  gaseous  states,  in  which  heat  dis- 
appeared— at  any  rate,  as  regards  the  thermometer.  But 
when  the  gaseous  body  was  restored  to  the  liquid,  and  the 
liquid  to  the  solid  state,  exactly  the  same  quantity  of  heat 
reappeared  which  formerly  seemed  to  have  been  lost. 
Heat  was  said  to  have  become  latent.  On  this  view,  liquid 
water  differed  from  solid  ice  in  containing  a  certain 
quantity  of  heat  bound,  which,  just  because  it  was  bound, 
could  not  pass  to  the  thermometer,  and  therefore  was  not 
indicated  by  it.  Aqueous  vapour  contains  a  far  greater 
quantity  of  heat  thus  boimd.  But  if  the  vapour  be  pre- 
cipitated, and  the  liquid  water  restored  to  the  state  of 
ic3,  exactly  the  same  amount  of  heat  is  liberated  as  had 
become  latent  in  the  melting  of  the  ice  and  in  the 
vaporisation  of  the  water. 

Finally,  heat  is  sometimes  produced  and  sometimes 
disappears  in  chemical  processes.  But  even  here  it  might 
be  assumed  that  the  various  chemical  elements  and 
chemical  compounds  contain  certain  constant  quantities 
of  latent  heat,  which,  when  they  change  their  composi- 
tion, are  sometimes  liberated  and  sometimes  must  be 
supplied  from  external  sources.  Accurate  experiments 
have  shown  that  the  quantity  of  heat  which  is  developed 
by  a  chemical  process,  for  instance,  in  burning  a  pound 
of  pure  carbon  into  carbonic  acid,  is  perfectly  con- 
stant, whether  the  combustion  is  slow  or  rapid,  whether 
it  takes 'place  all  at  once  or  by  intermediate  stages.  This 
also  a^;reed  very  well  with  the  assumption,  which  was  the 
basis  of  the  theory  of  heat,  that  heat  is  a  substance 
entirely  unchangeable  in  quantity.     The  natural  processes 


314  ON   THE    CONSERVATION   OF   FOECE. 

which  have  here  been  briefly  mentioned,  were  the  subject 
of  extensive  experimental  and  mathematical  investiga- 
tions, especially  of  the  great  French  physicists  in  the 
last  decade  of  the  former,  and  the  first  decade  of  the 
present,  century  ;  and  a  rich  and  accurately-worked  chapter 
of  physics  had  been  developed,  in  which  everything  agreed 
excellently  with  the  hjrpothesis — that  heat  is  a  substance. 
On  the  other  hand,  the  invariability  in  the  quantity  of 
heat  in  all  these  processes  could  at  that  time  be  explained 
in  no  other  manner  than  that  heat  is  a  substance. 

But  one  relation  of  heat — namely,  that  to  mechanical 
work — had  not  been  accurately  investigated.  A  French 
engineer,  Sadi  Carnot,  son  of  the  celebrated  War  Minister 
of  the  Revolution,  had  indeed  endeavoured  to  deduce  the 
work  which  heat  performs,  by  assuming  that  the  hypo- 
thetical caloric  endeavoured  to  expand  like  a  gas  ;  and 
from  this  assumption  he  deduced  in  fact  a  remarkable 
law  as  to  the  capacity  of  heat  for  work,  which  even  now, 
though  with  an  essential  alteration  introduced  by  Clausius, 
is  among  the  bases  of  the  modern  mechanical  theory  of 
heat,  and  the  practical  conclusions  from  which,  so  far  as 
they  could  at  that  time  be  compared  with  experiments, 
have  held  good. 

But  it  was  already  known  that  whenever  two  bodies 
in  motion  rubbed  against  each  other,  heat  was  developed 
anew,  and  it  could  not  be  said  whence  it  came. 

The  fact  is  universally  recognised  ;  the  axle  of  a  car- 
riage which  is  badly  greased  and  where  the  friction  is 
great,  becomes  hot — so  hot,  indeed,  that  it  niay  take  fire  ; 
machine-wheels  with  iron  axles  going  at  a  great  rate  may 
become  so  hot  that  they  weld  to  their  sockets.  A  power- 
ful degree  of  friction  is  not,  indeed,  necessary  to  disen- 
gage an  appreciable  degree  of  heat ;  thus,  a  lucifer- 
match,  which  by  rubbing  is  so  heated  that  the  phosphoric 
mass  ignites,  teaches  this  fact.     Nay,  it  is  enough  to  rub 


ON    THE    CONSEKVATION    OF   FORCE.  345 

the  dry  hands  together  to  feel  the  heat  produced  by  fric- 
tion, and  which  is  far  greater  than  the  heating  which 
takes  place  when  the  hands  lie  gently  on  each  other. 
Uncivilized  people  use  the  friction  of  two  pieces  of  wood 
to  kindle  a  fire.  With  this  view,  a  sharp  spindle  of  hard 
wood  is  made  to  revolve  rapidly  on  a  base  of  soft  wood  in 
the  manner  represented  in  Fig.  47. 

Fig.  47. 


So  long  as  it  was  only  a  question  of  the  friction  of 
solids,  in  which  particles  from  the  surface  become  de- 
tached and  compressed,  it  might  be  supposed  that  some 
changes  in  structure  of  the  bodies  rubbed  might  here 
liberate  latent  heat,  which  would  thus  appear  as  heat  of 
friction. 

But  heat  can  also  be  produced  by  the  friction  of  liquids, 
in  which  there  could  be  no  question  of  changes  in  struc- 
ture, or  of  the  liberation  of  latent  heat.  The  first  de- 
cisive experiment  of  this  kind  was  made  by  Sir  Humphry 
Davy  in  the  commencement  of  the  present  century.     In 


346  ON   THE   CONSERVATION   OF   FORCE. 

a  cooled  space  he  made  two  pieces  of  ice  rub  against  each 
other,  and  thereby  caused  them  to  melt.  The  latent  heat 
which  the  newly  formed  water  must  have  here  assimilated 
could  not  have  been  conducted  to  it  by  the  cold  ice,  or 
Lave  been  produced  by  a  change  of  structure ;  it  could 
have  come  from  no  other  cause  than  from  friction,  and 
must  have  been  created  by  friction. 

Heat  can  also  be  produced  by  the  impact  of  imperfectly 
elastic  bodies  as  well  as  by  friction.  This  is  the  case,  for 
instance,  when  we  produce  fire  by  striking  flint  against 
steel,  or  when  an  iron  bar  is  worked  for  some  time  by 
powerful  blows  of  the  hammer. 

If  we  inquire  into  the  mechanical  effects  of  friction 
and  of  inelastic  impact,  we  find  at  once  that  these  are 
the  processes  by  wliich  all  terrestrial  movements  are 
brought  to  rest.  A  moving  body  whose  motion  was  not 
retarded  by  any  resisting  force  would  continue  to  move  to 
all  eternity.  The  motions  of  the  planets  are  an  instance 
of  this.  This  is  apparently  never  the  case  with  the  mo- 
tion of  the  terrestrial  bodies,  for  they  are  always  in  con- 
tact with  other  bodies  which  are  at  rest,  and  rub  against 
them.  We  can,  indeed,  very  much  diminish  their  fric- 
tion, but  never  completely  annul  it.  A  wheel  which  turns 
about  a  well-worked  axle,  once  set  in  motion  continues 
it  for  a  long  time ;  and  the  longer,  the  more  truly  and 
smoother  the  axle  is  made  to  turn,  the  better  it  is  greased, 
and  the  less  the  pressure  it  has  to  support.  Yet  the  vis 
viva  of  the  motion  which  we  have  imparted  to  such  a 
wheel  when  we  started  it,  is  gradually  lost  in  consequence 
of  friction.  It  disappears,  and  if  we  do  not  carefully 
consider  the  matter,  it  seems  as  if  the  vis  viva  which  the 
wheel  had  possessed  had  been  simply  destroyed  without 
any  substitute. 

A  bullet  which  is  rolled  on  a  smooth  horizontal  surface 
continues  to  roll  until  its  velocity  is  destroyed  by  fric- 


ON   THE   CONSERVATION   OP   FOECE.  347 

tion  on  the   path,  caused  by  the  very  minute  impacts 
on  its  little  roughnesses. 

A  pendulum  which  has  been  put  in  vibration  can  con- 
tinue to  oscillate  for  hours  if  the  suspension  is  good, 
without  being  driven  by  a  weight ;  but  by  the  friction 
against  the  surrounding  air,  and  by  that  at  its  place  of 
suspension,  it  ultimately  comes  to  rest. 

A  stone  which  has  fallen  from  a  height  has  acquired  a 
certain  velocity  on  reaching  the  earth  ;  this  we  know  is  the 
equivalent  of  a  mechanical  work  ;  so  long  as  this  velocity 
continues  as  such,  we  can  direct  it  upwards  by  means  of 
suitable  arrangements,  and  thus  utilise  it  to  raise  the 
stone  again.  Ultimately  the  stone  strikes  against  the 
earth  and  comes  to  rest ;  the  impact  has  destroyed  its 
velocity,  and  therewith  apparently  also  the  mechanical 
work  which  this  velocity  could  have  effected. 

If  we  review  the  result  of  all  these  instances,  which 
each  of  you  could  easily  add  to  from  your  own  daily  ex- 
perience, we  shall  see  that  friction  and  inelastic  impact 
are  processes  in  which  mechanical  work  is  destroyed,  and 
heat  produced  in  its  place. 

The  experiments  of  Joule,  which  have  been  already 
mentioned,  lead  us  a  step  further.  He  has  measured  in 
foot  pounds  the  amount  of  work  which  is  destroyed  by  the 
friction  of  solids  and  by  the  friction  of  liquids ;  and,  on 
the  other  hand,  he  has  determined  the  quantity  of  heat 
which  is  thereby  produced,  and  has  established  a  definite 
relation  between  the  two.  His  experiments  show  tliat 
when  heat  is  produced  by  the  consumption  of  work,  a 
definite  quantity  of  work  is  required  to  produce  that 
amount  of  heat  which  is  known  to  physicists  as  the  unit 
of  heat ;  the  heat,  that  is  to  say,  which  is  necessary  to 
raise  one  gramme  of  water  through  one  degree  centigrade. 
The  quantity  of  wcrk  necessary  for  this  is,  according  to 
Joule's  best  experiments,  equal  to  the  work  which  a 
16 


348  ON   THE   CONSERVATION   OP   FOECE. 

gramme  would  perform  in  falling  through  a  height  of 
425  metres. 

In  order  to  show  how  closely  concordant  are  his 
numbers,  I  will  adduce  the  results  of  a  few  series  of 
experiments  which  he  obtained  after  introducing  the 
latest  improvements  in  his  methods. 

1.  A  series  of  experiments  in  which  water  was  heated 
by  friction  in  a  brass  vessel.  In  the  interior  of  this 
vessel  a  vertical  axle  provided  with  sixteen  paddles  was 
rotated,  the  eddies  thus  produced  being  broken  by  a  series 
of  projecting  barriers,  in  which  parts  were  cut  out  large 
enough  for  the  paddles  to  pass  through.  The  value  of 
the  equivalent  was  424*9  metres. 

2.  Two  similar  experiments,  in  which  mercury  in  an 
iron  vessel  was  substituted  for  water  in  a  brass  one,  gave 
425  and  426-3  metres. 

3.  Two  series  of  experiments,  in  which  a  conical  ring 
rubbed  against  another,  both  surrounded  by  mercury, 
gave  426*7  and  425*6  metres. 

Exactly  the  same  relations  between  heat  and  work 
were  also  found  in  the  reverse  process — that  is,  when 
work  was  produced  by  heat.  In  order  to  execute  this 
process  under  physical  conditions  that  could  be  controlled 
as  perfectly  as  possible,  permanent  gases  and  not  vapours 
were  used,  although  the  latter  are,  in  practice,  more  con- 
venient for  producing  large  quantities  of  work,  as  in  the 
case  of  the  steam-engine.  A  gas  which  is  allowed  to 
expand  with  moderate  velocity  becomes  cooled.  Joule 
was  the  first  to  show  the  reason  of  this  cooling.  For  the 
gas  has,  in  expanding,  to  overcome  the  resistance,  which 
the  pressure  of  the  atmosphere  and  the  slowly  yielding 
side  of  the  vessel  oppose  to  it ;  or,  if  it  cannot  of  itself 
overcome  this  resistance,  it  supports  the  arm  of  the 
observer  which  does  it.  Gas  thus  performs  work,  and 
this  work  is  produced  at  the  cost  of  its  heat.     Hence  the 


ON  THE   CONSERVATION   OF   FORCE.  349 

cooling.  If,  on  the  contrary,  the  gas  is  suddenly  allowed 
to  issue  into  a  perfectly  exhausted  space  where  it  finds  no 
resistance,  it  does  not  become  cool  as  Joule  has  shown  ; 
or  if  iudividual  parts  of  it  become  cool,  others  become 
warm  ;  and,  after  the  temperature  has  become  equalised, 
this  is  exactly  as  much  as  before  the  sudden  expansion  of 
the  gaseous  mass. 

How  much  heat  the  various  gases  disengage  when  they 
are  compressed,  and  how  much  work  is  necessary  for  their 
compression  ;  or,  conversely,  how  much  heat  disappears 
when  they  expand  under  a  pressure  equal  to  their  own 
counterpressure,  and  how  much  work  they  thereby  effect  in 
overcoming  this  counterpressure,  was  partly  known  from 
the  older  physical  experiments,  and  has  partly  been  de- 
termined by  the  recent  experiments  of  Eegnault  by 
extremely  perfect  methods.  Calculations  with  the  best 
data  of  this  kind  give  us  the  value  of  the  thermal  equiva- 
lent from  experiments : — 

With  atmospheric  air 4260  metres. 

„     oxygen 4257       „ 

„     nitrogen 431*3       „ 

„     hydrogen 425-3       „ 

Comparing  these  numbers  with  those  which  determine 
the  equivalence  of  heat  and  mechanical  work  in  friction, 
as  close  an  agreement  is  seen  as  can  at  all  be  expected 
from  numbers  which  have  been  obtained  by  such  varied 
investigations  of  different  observers. 

Thus  then :  a  certain  quantity  of  heat  may  be  changed 
into  a  definite  quantity  of  work  ;  this  quantity  of  work  can 
also  be  retransformed  into  heat,  and,  indeed,  into  exactly 
the  same  quantity  of  heat  as  that  from  which  it  origi- 
nated ;  in  a  mechanical  point  of  view,  they  are  exactly 
equivalent.  Heat  is  a  new  form  in  which  a  quantity  of 
•work  may  appear. 

These  facts  no  longer  permit  us  to   regard  heat  as  a 


350      ON  THE  CONSERVATIOX  OF  FORCE. 

substance,  for  its  quantity  is  not  unchangeable.  It  can 
be  produced  anew  from  the  vis  viva  of  motion  destroyed  ; 
it  can  be  destroyed,  and  then  produces  motion.  We  must 
rather  conclude  from  this  that  heat  itself  is  a  motion,  an 
internal  invisible  motion  of  the  smallest  elementary  par- 
ticles of  bodies.  If,  therefore,  motion  seems  lost  in 
friction  and  impact,  it  is  not  actually  lost,  but  only  passes 
from  the  great  visible  masses  to  their  smallest  particles  ; 
while  in  steam-engines  the  internal  motion  of  the  heated 
gaseous  particles  is  transferred  to  the  piston  of  the 
machine,  accumulated  in  it,  and  combined  in  a  resultant 
whole. 

But  what  is  the  nature  of  tliis  internal  motion,  can  only 
be  asserted  with  any  degree  of  probability  in  the  case  of 
gases.  Their  particles  probably  cross  one  another  in 
rectilinear  paths  in  all  directions,  until,  striking  another 
particle,  or  against  the  side  of  the  vessel,  they  are  re- 
flected in  another  direction.  A  gas  would  thus  be 
analogous  to  a  swarm  of  gnats,  consisting,  however,  of 
particles  infinitely  small  and  infinitely  more  closely 
packed.  This  hypothesis,  which  has  been  developed  by 
Kronig,  Clausius,  and  Maxwell,  very  well  accounts  for  all 
the  phenomena  of  gases. 

What  appeared  to  the  earlier  physicists  to  be  the  con- 
stant quantity  of  heat  is  nothing  more  than  the  whole 
motive  power  of  the  motion  of  heat,  which  remains  con- 
stant so  long  as  it  is  not  transformed  into  other  forms  of 
work,  or  results  afresh  from  them. 

We  turn  now  to  another  kind  of  natural  forces  which 
can  produce  work — I  mean  the  chemical.  We  have  to- 
day already  come  across  them.  They  are  the  ultimate 
cause  of  the  work  which  gunpowder  and  the  steam-engine 
produce  ;  for  the  heat  which  is  consumed  in  the  latter, 
for  example,  originates  in  the  combustion  of  carbon  — 
that  is  to  say,  in  a  chemical  process.     The  burning  of 


ON   THE   CONSERVATION   OF  FORCE.  351 

coal  is  the  chemical  union  of  carbon  with  the  oxygen  of 
the  air,  taking  place  under  the  influence  of  the  chemical 
affinity  of  the  two  substances. 

We  may  regard  this  force  as  an  attractive  force  between 
the  two,  which,  however,  only  acts  through  them  with 
extraordinary  power,  if  the  smallest  particles  of  the  two 
substances  are  in  closest  proximity  to  each  other.  In 
combustion  this  force  acts  ;  the  carbon  and  oxygen  atoms 
strike  against  each  other  and  adhere  firmly,  inasmuch  as 
they  form  a  new  compound — carbonic  acid — a  gas  knowm 
to  all  of  you  as  that  which  ascends  from  all  fermenting 
and  fermented  liquids — from  beer  and  champagne.  Now 
this  attraction  between  the  atoms  of  carbon  and  of  oxygen 
performs  work  just  as  much  as  that  which  the  earth  in  the 
form  of  gravity  exerts  upon  a  raised  weight.  When  the 
weight  falls  to  the  ground,  it  produces  an  agitation,  which 
is  partly  transmitted  to  the  vicinity  as  sound  waves,  and 
partly  remains  as  the  motion  of  heat.  The  same  result 
we  must  expect  from  chemical  action.  When  carbon  and 
oxygen  atoms  have  rushed  against  each  other,  the  newly- 
formed  particles  of  carbonic  acid  must  be  in  the  most 
violent  molecular  motion — that  is,  in  the  motion  of  heat. 
And  this  is  so.  A  pound  of  carbon  burned  with  oxygen  to 
form  carbonic  acid,  gives  as  much  heat  as  is  necessary  to 
raise  80*9  pounds  of  water  from  the  freezing  to  the 
boiling  point ;  and  just  as  the  same  amount  of  work  is 
produced  when  a  weight  falls,  whether  it  falls  slowly  or 
fast,  so  also  the  same  quantity  of  heat  is  produced  by  the 
combustion  of  carbon,  whether  this  is  slow  or  rapid, 
whether  it  takes  place  all  at  once,  or  by  successive  stages. 

When  the  carbon  is  burned,  we  obtain  in  its  stead,  and 
in  that  of  the  oxygen,  the  gaseous  product  of  combustion 
carbonic  acid.  Immediately  after  combustion  it  is  in- 
candescent. When  it  has  afterwards  imparted  heat  to  the 
vicinity,  we  have  in  the  carbonic  acid  the  entire  quantity 


352  ON   THE   COl^SERVATION"   OF   FORCE. 

of  carbon  and  the  entire  quantity  of  oxygen,  and  also  the 
force  of  affinity  quite  as  strong  as  before.  But  the  action 
of  the  latter  is  now  limited  to  holding  the  atoms  of 
carbon  and  oxygen  firmly  united ;  they  can  no  longer 
proiuce  either  heat  or  work  any  more  than  a  fallen 
weight  can  do  work  if  it  has  not  been  again  raised 
by  some  extraneous  force.  When  the  carbon  has  been 
burnt  we  take  no  further  trouble  to  retain  the  car- 
bonic acid ;  it  can  do  no  more  service,  we  endeavour 
to  get  it  out  of  the  chimneys  of  our  houses  as  fast  as  we 
can. 

Is  it  possible,  then,  to  tear  asunder  the  particles  of 
carbonic  acid,  and  give  to  them  once  more  the  capacity  of 
work  which  they  had  before  they  were  combined,  just  as 
we  can  restore  the  potentiality  of  a  weight  by  raising  it 
from  the  ground  ?  It  is  indeed  possible.  We  shall  after- 
wards see  how  it  occurs  in  the  life  of  plants ;  it  can  also 
be  effected  by  inorganic  processes,  though  in  roundabout 
ways,  the  explanation  of  which  would  lead  us  too  far  from 
our  present  course. 

This  can,  however,  be  easily  and  directly  shown  for 
another  element,  hydrogen,  which  can  be  burnt  just  like 
carbon.  Hydrogen  with  carbon  is  a  constituent  of  all 
combustible  vegetable  substances,  among  others,  it  is  also 
an  essential  constituent  of  the  gas  which  is  used  for 
lighting  our  streets  and  rooms;  in  the  free  state  it  is 
also  a  gas,  the  lightest  of  all,  and  burns  when  ignited 
with  a  feebly  luminous  blue  flame.  In  this  combustion — 
that  is,  in  the  chemical  combination  of  hydrogen  with 
oxygen,  a  very  considerable  quantity  of  heat  is  produced  ; 
for  a  given  weight  of  hydrogen,  four  times  as  much  heat 
as  in  the  combustion  of  the  same  weight  of  carbon.  The 
product  of  combustion  is  water,  which,  therefore,  is  not  of 
itself  further  combustible,  for  the  hjdrogen  in  it  is  com- 
pletely  saturated   with   oxygen.      The  force  of  affinity, 


ON   THE   CONSERVATION   OF   FORCE.  353 

therefore,  of  bydrogen  for  oxygen,  like  that  of  carbon  for 
oxygen,  performs  work  in  combustion,  which  appeals  in 
the  form  of  heat.  In  the  water  which  has  been  formed 
during  combustion,  the  force  of  affinity  is  exerted  between 
the  elements  as  before,  but  its  capacity  for  work  is  lost. 
Hence  the  two  elements  must  be  again  separated,  their 
atoms  torn  apart,  if  new  effects  are  to  be  produced  from 
them. 

This  we  can  do  by  the  aid  of  currents  of  electricity. 
In  the  apparatus  depicted  in  Fig.  48,  we  have  two  glass 

Fig.  48. 


vessels  filled  with  acidulated  water,  a  and  a^,  which  are 
separated  in  the  middle  by  a  porous  plate  moistened  with 
water.  In  both  sides  are  fitted  platinum  wires,  k,  which 
are  attached  to  platinum  plates,  i  and  i^  As  soon  as  a 
galvanic  current  is  transmitted  through  the  water  by  the 
platinum  wires,  k,  you  see  bubbles  of  gas  ascend  from 
the  plates  i  and  i'.  These  bubbles  are  the  two  elements 
of  water,  hydrogen  on  the  one  hand,  and  oxygen  on  the 
other.  The  gases  emerge  through  the  tubes  g  and  g^ 
If  we  wait  until  the  upper  part  of  the  vessels  and  the 
tubes  have  been  filled  with  it,  we  can  inflame  hydrogen 
at  one  side  ;  it  burns  with  a  blue  flame.  If  I  bring  a 
glimmering  spill  near  the  mouth  of  the  other  tube  it 


354 


ON   THE   COXSERYATIOIS'   OF   FORCE. 


bursts  into  flame,  just  as  happens  with  oxygen  gas,  in 
which  the  processes  of  combustion  are  far  more  intense 
than  in  atmospheric  air,  where  the  oxygen  mixed  with 
nitrogen  is  only  one-fifth  of  the  whole  volume. 

If  I  hold  a  glass  flask  filled  with  water  over  the  hydro- 
gen flame,  the  water,  newly  formed  in  combustion,  con- 
denses upon  it. 

If  a  platinum  wire  be  held  in  the  almost  non-luminous 
flame,  you  see  how  intensely  it  is  ignited  ;  in  a  plentiful 
current  of  a  mixture  of  the  gases,  hydrogen  and  oxygen, 
which  have  been  liberated  in  the  above  experiment,  the 

Fig.  49. 


almost  infusible  platinum  might  even  be  melted.  The 
hydrogen  which  has  here  been  liberated  from  the  water 
by  the  electrical  current  has  regained  the  capacity  of 
producing  large  quantities  of  heat  by  a  fresh  combination 
with  oxygen  ;  its  affinity  for  oxygen  has  regained  for  it 
its  capacity  for  work. 

We  here  become  acquainted  with  a  new  source  of 
work,  the  electric  current  which  decomposes  water.  This 
current  is  itself  produced  by  a  galvanic  battery.  Fig.  49. 


ON  THE   COXSERVATION  OF  FOHCE.  355 

Each  of  the  four  vessels  contains  nitric  acid,  in  which 
there  is  a  hollow  cylinder  of  very  compact  carbon.  In 
the  middle  of  the  carbon  cylinder  is  a  cylindrical  porous 
vessel  of  while  clay,  which  contains  dilute  sulphuric  acid; 
in  this  dips  a  zinc  cylinder.  Each  zinc  cylinder  is  con- 
nected by  a  metal  ring  with  the  carbon  cylinder  of  the 
next  vessel,  the  last  zinc  cylinder  n  is  connected  with  one 
platinum  plate,  and  the  first  carbon  cylinder,  p,  with  the 
other  platinum  plate  of  the  apparatus  for  the  decomposi- 
tion of  water. 

If  now  the  conducting  circuit  of  this  galvanic  appa- 
ratus is  completed,  and  the  decomposition  of  water  begins, 
a  chemical  process  takes  place  simultaneously  in  the  cells 
of  the  voltaic  battery.  Zinc  takes  oxygen  from  the  sur- 
rounding water  and  undergoes  a  slow  combustion.  The 
product  of  combustion  thereby  produced,  oxide  of  zinc, 
unites  further  with  sulphuric  acid,  for  which  it  has  a 
powerful  affinity,  and  sulphate  of  zinc,  a  saline  kind  of 
substance,  dissolves  in  the  liquid.  The  oxygen,  moreover, 
which  is  withdrawn  from  it  is  taken  by  the  water  from 
the  nitric  acid  surrounding  the  cylinder  of  carbon,  which 
is  very  rich  in  it,  and  readily  gives  it  up.  Thus,  in  tlie 
galvanic  battery  zinc  burns  to  sulphate  of  zinc  at  ilie  cost 
of  the  oxygen  of  nitric  acid. 

Thus,  while  one  product  of  combustion,  water,  is  again 
separated,  a  new  combustion  is  taking  place— that  of 
zinc.  While  we  there  reproduce  chemical  affinity  which 
is  capable  of  work,  it  is  here  lost.  The  electrical  current 
is,  as  it  were,  only  the  carrier  which  transfers  the  chemical 
force  of  the  zinc  uniting  with  oxygen  and  acid  to  water 
in  the  decomposing  cell,  and  uses  it  for  overcoming  the 
chemical  force  of  hydrogen  and  oxygen. 

In  this  case,  we  can  restore  work  which  has  been  lost, 
but  only  by  using  another  force,  that  of  oxidising  zinc. 

Here  we  have  overcome  chemical  forces  by  chemical 


356 


0^  THE   COXSERVATIOX   OF   FORCE. 


forces,  through  the  instrumentality  of  the  electrical  cur- 
rent.    But  we  can  attain  the  same  object  by  mechanical 

Fig.  50. 


forces,  if  we  produce  the  electrical  current  by  a  magneto- 
electrical  machine,  Fig.  50.  If  we  turn  the  handle,  the 
anker  E  E^,  on  which  is  coiled  copper-wire,  rotates  in  froDt 


ON   THE   CONSERVATION   OF   FORCE.  357 

of  the  poles  of  the  horse-shoe  magnet,  and  in  these  coils 
electrical  currents  are  produced,  which  can  be  led  from 
the  points  a  and  b.  If  the  ends  of  these  wires  are  con- 
nected with  the  apparatus  for  decomposing  water  we 
obtain  hydrogen  and  oxygen,  though  in  far  smaller  quan- 
tity than  by  the  aid  of  the  battery  which  we  used  before. 
But  this  process  is  interesting,  for  the  mechanical  force 
of  the  arm  which  turns  the  wheel  produces  the  work  which 
is  required  for  separating  the  combined  chemical  ele- 
ments. Just  as  the  steam-engine  changes  chemical  into 
mechanical  force,  the  magneto-electrical  machine  trans- 
forms mechanical  force  into  chemical. 

The  application  of  electrical  currents  opens  out  a  large 
number  of  relations  between  the  various  natural  forces. 
We  have  decomposed  water  into  its  elements  by  such 
currents,  and  should  be  able  to  decompose  a  large  number 
of  other  chemical  compounds.  On  the  other  hand,  in 
ordinary  galvanic  batteries  electrical  currents  are  produced 
by  chemical  forces. 

In  all  conductors  through  which  electrical  currents 
pass  they  produce  heat ;  I  stretch  a  thin  platinum  wire 
between  the  ends  n  and  p  of  the  galvanic  battery.  Fig.  49 ; 
it  becomes  ignited  and  melts.  On  the  other  hand,  elec- 
trical currents  are  produced  by  heat  in  what  are  called 
thermo-electric  elements. 

Iron  which  is  brought  near  a  spiral  of  copper  wire, 
traversed  by  an  electrical  current,  becomes  magnetic, 
and  then  attracts  other  pieces  of  iron,  or  a  suitably 
placed  steel  magnet.  We  thus  obtain  mechanical  actions 
which  meet  with  extended  applications  in  the  electrical 
telegraph,  for  instance.  Fig.  51  represents  a  Morse's 
telegraph  in  one-third  of  the  natural  size.  The  essential 
part  is  a  horse-shoe  shaped  iron  core,  which  stands  in  the 
copper  spirals  b  b.  Just  over  the  top  of  this  is  a  small 
steel   magnet   c  c,   which   is    attracted   the  moment    an 


35S 


Oy  THE   COXSERVATIOX   OF  FORCE. 


electrical  current,  arriving  by  the  telegraph  wire,  traverses 
the  spirals  b  b.  The  magnet  c  c  is  rigidly  fixed  in  the 
lever  d  d,  at  the  other  end  of  which  is  a  style ;  this 
makes  a  mark  on  a  paper  band,  drawn  by  a  clock-work,  as 
often  and  as  long  as  c  c  is  attracted  by  the  magnetic 
action  of  the  electrical  cuiTent.  Conversely,  by  reversing 
the  magnetism  in  the  iron  core  of  the  spirals  b  b,  we 
should  obtain  in  them  an   electrical  current  just  as  we 

Fig.  61. 


have  obtained  such  currents  in  the  magneto-electrical 
machine,  Fig.  50 ;  in  the  spirals  of  that  machine  there  is 
an  iron  core  which,  by  being  approached  to  the  poles  of 
the  large  horse-shoe  magnet,  is  sometimes  magnetised  in 
one  and  sometimes  in  the  other  direction. 

I  will  not  accumulate  examples  of  such  relations; 
in  subsequent  lectures  we  shall  come  across  them.  Let 
us  review  these  examples  once  more,  and  recognise  in 
them  the  law  which  is  common  to  all. 


ON  THE  CONSERVATION  OF  FORCE.      359 

A  raised  weight  can  produce  work,  but  in  doing  so  it 
must  necessarily  sink  from  its  height,  and,  when  it  has 
fallen  as  deep  as  it  can  fall,  its  gravity  remains  as  before, 
but  it  can  no  longer  do  work. 

A  stretched  spring  can  do  work,  but  in  so  doing  it 
becomes  loose.  The  velocity  of  a  moving  mass  can  do 
work,  but  in  doing  so  it  comes  to  rest.  Heat  can  perform 
work  ;  it  is  destroyed  in  the  operation.  Chemical  forces 
can  perform  wc-rk,  but  they  exhaust  themselves  in  the 
effort. 

Electrical  currents  can  perform  work,  but  to  keep  them 
up  we  must  consume  either  chemical  or  mechanical  forces, 
or  heat. 

We  may  express  this  generally.  It  is  a  universal 
character  of  all  knoiun  natural  forces  that  their  capacity 
for  work  is  exhausted  in  the  degree  in  which  they  actu- 
ally perform  work. 

We  have  seen,  further,  that  when  a  weight  fell  without 
performing  any  work,  it  either  acquired  velocity  or  pro- 
duced heat.  We  might  also  drive  a  magneto-electrical 
machine  by  a  falling  weight ;  it  would  then  furnish  elec- 
trical currents. 

We  have  seen  that  chemical  forces,  when  they  come 
into  play,  produce  either  heat  or  electrical  currents  or 
mechanical  work. 

We  have  seen  that  heat  may  be  changed  into  work ; 
there  are  apparatus  (thermo-electric  batteries)  in  which 
electrical  currents  are  produced  by  it.  Heat  can  directly 
separate  chemical  compounds  ;  thus,  when  we  burn  lime- 
stone, it  separates  carbonic  acid  from  lime. 

Thus,  whenever  the  capacity  for  work  of  one  natural 
force  is  destroyed,  it  is  transformed  into  another  kind  of 
activity.  Even  within  the  circuit  of  inorganic  natural 
forces,  we  can  transform  each  of  them  into  an  active 
condition  by  the  aid  of  any  other  natural  force  which  is 


S60  ON  THE   CONSEHTATION   OF   FORCE. 

capable  of  work.  The  connections  between  the  various 
natural  forces  which  modern  physics  has  revealed,  are  so 
extraordinarily  numerous  that  several  entirely  different 
methods  may  be  discovered  for  each  of  these  problems. 

I  have  stated  how  we  are  accustomed  to  measure 
mechanical  work,  and  how  the  equivalent  in  work  of  heat 
may  be  found.  The  equivalent  in  work  of  chemical 
processes  is  again  measured  by  the  heat  which  they  pro- 
duce. By  similar  relations,  the  equivalent  in  work  of  the 
other  natural  forces  may  be  expressed  in  terms  of  mechani- 
cal work. 

If,  now,  a  certain  quantity  of  mechanical  work  is  lost, 
there  is  obtained,  as  experiments  made  with  the  object  of 
determining  this  point  show,  an  equivalent  quantity  of 
heat,  or,  instead  of  this,  of  chemical  force  ;  and,  conversely, 
when  heat  is  lost,  we  gain  an  equivalent  quantity  of 
chemical  or  mechanical  force ;  and,  again,  when  chemical 
force  disappears,  an  equivalent  of  heat  or  work ;  so  that 
in  all  these  interchanges  between  various  inorganic  natural 
forces  working  force  may  indeed  disappear  in  one  form, 
but  then  it  reappears  in  exactly  equivalent  quantity  in 
some  other  form  ;  it  is  thus  neither  increased  nor  dimi- 
nished, but  always  remains  in  exactly  the  same  quantity. 
We  shall  subsequently  see  that  the  same  law  holds  good 
also  for  processes  in  organic  nature,  so  far  as  the  facts 
have  been  tested. 

It  follows  thence  that  the  total  quantity  of  all  the  forces 
capable  of  work  m  the  whole  universe  remains  eternal 
and  unchanged  throughout  all  their  changes.  All  change 
in  nature  amounts  to  this,  that  force  can  change  its  form 
and  locality  without  its  quantity  being  changed.  The 
universe  possesses,  once  for  all,  a  store  of  force  which  is 
not  altered  by  any  change  of  phenomena,  can  neither  be 
increased  nor  diminished,  and  which  maintains  any  change 
which  takes  place  on  it. 


ON  THE  CONSEHVATION  OF  FORCE.      361 

You  see  how,  starting  from  considerations  based  on  the 
immediate  practical  interests  of  technical  work,  we  have 
been  led  up  to  a  universal  natural  law,  which,  as  far  as 
all  previous  experience  extends,  rules  and  embraces  all 
natural  processes ;  which  is  no  longer  restricted  to  the 
practical  objects  of  human  utility,  but  expresses  a  per- 
fectly general  and  particularly  characteristic  property  of 
all  natural  forces,  and  which,  as  regards  generality,  is 
to  be  placed  by  the  side  of  the  laws  of  the  unalter- 
ability  of  mass,  and  the  unalterability  of  the  chemical 
elements. 

At  the  same  time,  it  also  decides  a  great  practical 
question  which  has  been  much  discussed  in  the  last  two 
centuries,  to  the  decision  of  which  an  infinity  of  experi- 
ments have  been  made  and  an  infinity  of  apparatus  con- 
structed— that  is,  the  question  of  the  possibility  of  a  per- 
petual motion.  By  this  was  understood  a  machine  which 
was  to  work  continuously  without  the  aid  of  any  external 
driving  force.  The  solution  of  this  problem  promised 
enormous  gains.  Such  a  machine  would  have  had  all  the 
advantages  of  steam  without  requiring  the  expenditure  of 
fuel.  Work  is  wealth.  A  machine  which  could  produce 
work  from  nothing  was  as  good  as  one  which  made  gold. 
This  problem  had  thus  for  a  long  time  occupied  the  place 
of  gold  making,  and  had  confused  many  a  pondering 
brain.  That  a  perpetual  motion  could  not  be  produced 
by  the  aid  of  the  then  known  mechanical  forces  could  be 
demonstrated  in  the  last  century  by  the  aid  of  the  mathe- 
matical mechanics  which  had  at  that  time  been  developed. 
But  to  show  also  that  it  is  not  possible  even  if  heat, 
chemical  forces,  electricity,  and  mag-netism  were  made  to 
co-operate,  could  not  be  done  without  a  knowledge  of 
our  law  in  all  its  generality.  The  possibility  of  a  per- 
petual motion  was  first  finally  negatived  by  the  law  of 
the  conservation  of  force,  and  this  law  might  also  be  ex- 


302  ox  THE   COXSERTATIOJf   OF  FOKCE. 

pressed  in  the  practical  form  that  no  perpetual  motion  is 
possible,  that  force  cannot  be  produced  from  nothing ; 
something  must  be  consumed. 

You  will  only  be  ultimately  able  to  estimate  the  im- 
portance and  the  scope  of  our  law  when  you  have  before 
your  eyes  a  series  of  its  applications  to  individual  processes 
on  nature. 

What  I  have  to-day  mentioned  as  to  the  origin  of  the 
moving  forces  which  are  at  our  disposal,  directs  us  to 
something  beyond  the  narrow  confines  of  our  laboratories 
and  our  manufactories,  to  the  great  operations  at  work  in 
the  life  of  the  earth  and  of  the  universe.  The  force  of 
falling  water  can  only  flow  down  from  the  hills  when  rain 
and  snow  bring  it  to  them.  To  furnish  these,  we  must 
have  aqueous  vapour  in  the  atmosphere,  which  can  only 
be  effected  by  the  aid  of  heat,  and  this  heat  comes  from 
the  sun.  The  steam-engine  needs  the  fuel  which  the 
vegetable  life  yields,  whether  it  be  the  still  active  life  of 
the  surrounding  vegetation,  or  the  extinct  life  which  has 
produced  the  immense  coal  deposits  in  the  depths  of  the 
earth.  The  forces  of  man  and  animals  must  be  restored 
by  nourishment ;  all  nourishment  comes  ultimately  from 
the  vegetable  kingdom,  and  leads  us  back  to  the  same 
source. 

You  see  then  that  when  we  inquire  into  the  origin  of 
the  moving  forces  which  we  take  into  our  service,  we  are 
thrown  back  upon  the  meteorological  processes  in  the 
earth's  atmosphere,  on  the  life  of  plants  in  general,  and 
on  the  sun. 


THE  AIM  AM)  PEOGEISS  OF 
PHYSICAL  SCIENCE. 

AN   OPENING   ADDRESS   DELIVERED   AT    THE  NATURFOESCHER 
YERSAMMLUNG,   IN    INNSBRTJCK,   1869. 


In  accepting  the  honour  you  have  done  me  in  request- 
ing me  to  deliver  the  first  lecture  at  the  opening  meeting 
of  this  year's  Association,  it  appears  to  me  to  be  more  in 
keeping  with  the  import  of  the  moment  and  the  dignity  of 
this  assembly  that,  in  place  of  dealing  with  any  particular 
line  of  research  of  my  own,  I  should  invite  you  to  cast  a 
glance  at  the  development  of  all  the  branches  of  physical 
science  represented  on  these  occasions.  These  branches 
include  a  vast  area  of  special  investigation,  material 
of  almost  too  varied  a  character  for  comprehension,  the 
range  and  intrinsic  value  of  which  become  greater  with 
each  year,  while  no  bounds  can  be  assigned  to  its  increase. 
During  the  first  half  of  the  present  century  we  had  an 
Alexander  von  Humboldt,  who  was  able  to  scan  the 
scientific  knowledge  of  his  time  in  its  details,  and  to  bring 
it  within  one  vast  generalisation.  At  the  present  juncture, 
it  is  obviously  very  doubtful  whether  this  task  could  be 
accomplished  in  a  similar  way,  even  by  a  mind  with  gifts 
so  peculiarly  suited  for  the  purpose  as  Humboldt's  was, 
and  if  all  his  time  and  work  were  devoted  to  the  purpose. 
We.  however,  working  as  we  do  to  advance  a  single 


364     AIM   AKD   PROGEESS   OF   PHYSICAL   SCIENCE. 

department  of  science,  can  devote  but  little  of  our  time 
to  the  simultaneous  study  of  the  other  branches.  As 
soon  as  we  enter  upon  any  investigation,  all  our  powers 
have  to  be  concentrated  on  a  field  of  narrowed  limit.  We 
have  not  only,  like  the  philologian  or  historian,  to  seek 
out  and  search  through  books  and  gather  from  them  what 
others  have  already  determined  about  the  subject  under 
inquiry ;  that  is  but  a  secondary  portion  of  our  work. 
We  have  to  attack  the  things  themselves,  and  in  doing  so 
each  offers  new  and  peculiar  difficulties  of  a  kind  quite 
different  from  those  the  scholar  encounters ;  while  in  the 
majority  of  instances,  most  of  our  time  and  labour  is  con- 
sumed by  secondary  matters  that  are  but  remotely  con- 
nected with  the  purpose  of  the  investigation. 

At  one  time,  we  have  to  study  the  errors  of  our  instru- 
ments, with  a  view  to  their  diminution,  or,  where  they 
cannot  be  removed,  to  compass  their  detrimental  influ- 
ence ;  while  at  other  times  we  have  to  watch  for  the 
moment  when  an  organism  presents  itself  under  circum- 
stances most  favourable  for  research.  Again,  in  the  course 
of  our  investigation  we  learn  for  the  first  time  of  possible 
errors  which  vitiate  the  result,  or  perhaps  merely  raise  a 
suspicion  that  it  may  be  vitiated,  and  we  find  ourselves 
compelled  to  begin  the  work  anew,  till  every  shadow  of 
doubt  is  removed.  And  it  is  only  when  the  observer  takes 
such  a  grip  of  the  subject,  so  fixes  all  his  thoughts  and  all 
his  interest  upon  it  that  he  cannot  separate  himself  from 
it  for  weeks,  for  months,  even  for  years,  cannot  force 
himself  away  from  it,  in  short,  till  he  has  mastered  every 
detail,  and  feels  assured  of  all  those  results  which  must 
come  in  time,  that  a  perfect  and  valuable  piece  of  work 
is  done.  You  are  all  aware  that  in  every  good  research, 
the  preparation,  the  secondary  operations,  the  control  of 
possible  errors,  and  especially  in  the  separation  of  the 
results  attainable  in  the  time  from  those   that    cannot 


AIM   AND   PROGRESS   OF   PHYSICAL   SCIENCE.      365 

he  attained,  consume  far  more  time  than  is  really  re- 
quired to  make  actual  observations  or  experiments.  How 
much  more  ingenuity  and  thought  are  expended  in 
bringing  a  refractory  piece  of  brass  or  glass  into  sub- 
jection, than  in  sketching  out  the  plan  of  the  whole 
investigation !  Each  of  you  will  have  experienced  such 
impatience  and  over-excitement  during  work  where  all 
the  thoughts  are  directed  on  a  narrow  range  of  ques- 
tions, the  import  of  which  to  an  outsider  appears  trifling 
and  contemptible  because  he  does  not  see  the  end  to  which 
the  preparatory  work  tends.  I  believe  I  am  correct  in 
thus  describing  the  work  and  mental  condition  that  pre- 
cedes all  those  great  results  which  hastened  so  much  the 
development  of  science  after  its  long  inaction,  and  gave 
it  so  powerful  an  influence  over  every  phase  of  human 
life. 

The  period  of  work,  then,  is  no  time  for  broad  com- 
prehensive survey.  When,  however,  the  victory  over 
difficulties  has  happily  been  gained,  and  results  are  secured, 
a  period  of  repose  follows,  and  our  interest  is  next 
directed  to  examining  the  bearing  of  the  newly  esta- 
blished facts,  and  once  more  venturing  on  a  wider  survey 
of  the  adjoining  territory.  This  is  essential,  and  those 
only  who  are  capable  of  viewing  it  in  this  light  can 
hope  to  find  useful  starting-points  for  further  investi- 
gation. 

The  preliminary  work  is  followed  by  other  work,  treat- 
ing of  other  subjects.  In  the  course  of  its  different 
stages,  the  observer  will  not  deviate  far  from  a  direction 
of  more  or  less  narrowed  range.  F'or  it  is  not  alone  of 
importance  to  him  that  he  may  have  collected  information 
from  books  regarding  the  region  to  be  explored.  The 
human  memory  is,  on  the  whole,  proportionately  patient, 
and  can  store  up  an  almost  incredibly  large  amount  of 
learning.     In  addition,  however,  to  the  knowledge  which 


366     AIM   AND   PROGRESS   OF   PHYSICAL   SCIENCE. 

the  student  of  science  acquires  from  lectures  and  books, 
he  requires  intelligence  which  only  an  ample  and  diligent 
perception  can  give  him ;  he  needs  skill  which  comes 
only  by  repeated  experiment  and  long  practice.  His 
senses  must  be  sharpened  for  certain  kinds  of  observation, 
to  detect  minute  differences  of  form,  colour,  solidity, 
smell,  &c.,  in  the  object  under  examination ;  his  hand 
must  be  equally  trained  to  the  work  of  the  blacksmith, 
the  locksmith,  and  the  carpenter,  or  the  draughtsman  and 
the  violin-player,  and,  when  operating  with  the  micro- 
scope, must  surpass  the  lace-maker  in  delicacy  of  handling 
the  needle.  Moreover,  when  he  encounters  superior  de- 
structive forces,  or  performs  bloody  operations  upon  man 
or  beast,  he  must  possess  the  courage  and  coolness  of 
the  soldier.  Such  qualities  and  capabilities,  partly  the 
result  of  natural  aptitude,  partly  cultivated  by  long 
practice,  are  not  so  readily  and  so  easily  acquired  as  the 
mere  massing  of  facts  in  the  memory;  and  hence  it 
happens  that  an  investigator  is  compelled,  during  the 
entire  labours  of  his  life,  to  strictly  limit  his  field,  and  to 
confine  himself  to  those  branches  which  suit  him  best. 

We  must  not,  however,  forget  that  the  more  the  in- 
dividual worker  is  compelled  to  narrow  the  sphere  of  his 
activity,  so  much  the  more  will  his  intellectual  desires 
induce  him  not  to  sever  his  connection  with  the  subject 
in  its  entirety.  How  shall  he  go  stout  and  cheerful  to 
his  toilsome  work,  how  feel  confident  that  what  has  given 
him  so  much  labour  will  not  moulder  uselessly  away,  but 
remain  a  thing  of  lasting  value,  unless  he  keeps  alive 
within  himself  the  conviction  that  he  also  has  added  a 
fragment  to  the  stupendous  whole  of  Science  which  is 
to  make  the  reasonless  forces  of  nature  subservient  to 
the  moral  purposes  of  humanity  ? 

An  immediate  practical  use  cannot  generally  be  counted 
on  a  prioH  for  each  particular  investigation.     Physical 


AIM  AND  PROGRESS  OF   PHYSICAL   SCIENCE.      367 

science,  it  is  true,  has  by  the  practical  realisation  of  its 
results  transformed  the  entire  life  of  modern  humanity. 
But,  as  a  rule,  these  applications  appear  under  circum- 
stances when  they  are  least  expected ;  to  search  in  that 
direction  generally  leads  to  nothing  unless  certain  points 
have  already  been  definitely  fixed,  so  that  all  that  has  to 
be  done  is  to  remove  certain  obstacles  in  the  way  of  prac- 
tical application.  If  we  search  the  records  of  the  most 
important  discoveries,  they  are  either,  especially  in  earlier 
times,  made  by  workmen  who  their  whole  lives  through 
did  but  one  kind  of  work,  and,  either  by  a  happy  accident, 
or  by  a  searching,  repeated,  tentative  experiment,  hit 
upon  some  new  method  advantageous  to  their  particular 
handicraft ;  others  there  are,  and  this  is  especially  the 
case  in  most  of  the  recent  discoveries,  which  are  the 
fruit  of  a  matured  scientific  acquaintance  with  the  sub- 
ject in  question,  an  acquaintance  that  m  each  instance 
had  originally  been  acquired  without  any  direct  view  to 
possible  use. 

Our  Association  represents  the  whole  of  natural  science. 
To-day  are  assembled  mathematicians,  physicists,  chemists 
and  zoologists,  botanists  and  geologists,  the  teacher  of 
science  and  the  physician,  the  technologist  and  the  ama- 
teur who  finds  in  scientific  pursuits  relaxation  from  other 
occupation.  Here  each  of  us  hopes  to  meet  with  fresh 
impulse  and  encouragement  for  his  peculiar  work ;  the 
man  who  lives  in  a  small  country  place  hopes  to  meet 
with  the  recognition,  otherwise  unattaioable,  of  having 
aided  in  the  advance  of  science  ;  he  hopes  by  intercourse 
with  men  pursuing  more  or  less  the  same  object  to  mark 
the  aim  of  new  researches.  We  rejoice  to  find  among  us 
a  goodly  proportion  of  members  representing  the  culti- 
vated classes  of  the  nation  ;  we  see  influential  statesmen 
among  us.  They  all  have  an  interest  in  our  labours ; 
they  look  to  us  for  further  progress  in  civilisation,  fui'ther 


368     AIM   AND   PROGEESS   OF   PHYSICAL   SCIENCE. 

victories  over  the  powers  of  nature.  They  it  is  who 
place  at  our  disposal  the  actual  means  for  carrying  on  our 
labours,  and  are  therefore  entitled  to  enquire  into  the 
results  of  those  labours.  It  appears  to  me,  therefore, 
appropriate  to  this  occasion  to  take  account  of  the  pro- 
gress of  science  as  a  whole,  of  the  objects  it  aspires  to, 
and  the  magnitude  of  the  efforts  made  to  attain  them. 

Such  a  survey  is  desirable ;  that  it  lies  beyond  the 
powers  of  any  one  man  to  accomplish  with  even  an  ap- 
proximate completeness  such  a  task  as  this  is  clear  from 
what  I  have  already  said.  If  I  stand  here  to-day  with 
such  a  problem  entrusted  to  me,  my  excuse  must  be  that 
no  other  would  attempt  it,  and  I  hold  that  an  attempt  to 
accomplish  it,  even  if  with  small  success,  is  better  than 
none  whatever.  Besides,  a  physiologist  has  perhaps  more 
than  all  others  immediate  occasion  to  maintain  a  clear 
and  constant  view  of  the  entire  field,  for  in  the  present 
state  of  things  it  is  peculiarly  the  lot  of  the  physiologist 
to  receive  help  from  all  other  branches  of  science  and  to 
stand  in  alliance  with  them.  In  physiology,  in  fact,  the 
importance  of  the  vast  strides  to  which  I  shall  allude, 
has  been  chiefly  felt,  while  to  physiology,  and  the  leading 
controversies  arising  in  it,  some  of  the  most  valuable 
discoveries  are  directly  due. 

If  I  leave  considerable  gaps  in  my  survey,  my  excuse 
must  be  the  magnitude  of  the  task,  and  the  fact  that  the 
pressing  summons  of  my  friend  the  secretary  of  this  Asso- 
ciation reached  me  but  recently,  and  that  too  in  the  course 
of  my  summer  holiday  in  the  mountains.  The  gaps 
which  I  may  leave  will  at  all  events  be  abundantly  filled 
up  by  the  proceedings  of  the  Sections. 

Let  us  then  proceed  to  our  task.  In  discussing  the 
progress  of  physical  science  as  a  whole,  the  first  question 
which  presents  itself  is,  By  what  standard  are  we  to 
estimate  this  progress  ? 


AIM  AI!^D   PROGRESS   OF   PHYSICAL   SCIENCE.      369 

To  the  uninitiated,  this  science  of  ours  is  an  accumula- 
tion of  a  vast  number  of  facts,  some  of  which  are  con- 
spicuous for  their  practical  utility,  while  others  are 
merely  curiosities,  or  objects  of  wonder.  And,  if  it  were 
possible  to  classify  this  unconnected  mass  of  facts,  as  was 
done  in  the  Linnean  system,  or  in  encyclopaedias,  so  that 
each  may  be  readily  found  when  required,  such  knowledge 
as  this  would  not  deserve  the  name  of  science,  nor  satisfy 
either  the  scientific  wants  of  the  human  mind,  or  the 
desire  for  progressive  mastery  over  the  powers  of  nature. 
For  the  former  requires  an  intellectual  grasp  of  the  con- 
nection of  ideas,  the  latter  demands  our  anticipation  of  a 
result  in  cases  yet  untried,  and  under  conditions  that  we 
propose  to  introduce  in  the  course  of  our  experiment. 
Both  are  obviously  arrived  at  by  a  knowledge  of  the  law 
of  the  phenomena. 

Isolated  facts  and  experiments  have  in  themselves  no 
value,  however  great  their  number  may  be.  They  only  be- 
come valuable  in  a  theoretical  or  practical  point  of  view 
when  they  make  us  acquainted  with  the  law  of  a  series 
of  uniformly  recurring  phenomena,  or,  it  may  be,  cnly 
give  a  negative  result  showing  an  incompleteness  in  our 
knowledge  of  such  a  law,  till  then  held  to  be  perfect. 
From  the  exact  and  universal  conformity  to  law  of  natural 
phenomena,  a  single  observation  of  a  condition  that  we 
may  presume  to  be  rigorously  conformable  to  law,  suffices, 
it  is  true,  at  times  to  establish  a  rule  with  the  highest 
degree  of  probability ;  just  as,  for  example,  we  assume  our 
knowledge  of  the  skeleton  of  a  prehistoric  animal  to  be 
complete  if  we  find  only  one  complete  skeleton  of  a  single 
individual.  But  we  must  not  lose  sight  of  the  fact  that 
the  isolated  observation  is  not  of  value  m  that  it  is 
isolated,  but  because  it  is  an  aid  to  the  knowledge  of  the 
conformable  regularity  in  bodily  structure  of  an  entire 
species  of  organisms.     In  like  manner,  the  knowledge  of 


370     AIM   AND   PROGRESS   OF   PHYSICAL   SCIENCE. 

the  specific  heat  of  one  small  fragment  of  a  new  metal  is 
important  because  we  have  no  grounds  for  doubting  that 
any  other  pieces  of  the  same  metal  subjected  to  the  same 
treatment  will  yield  the  same  result. 

To  find  the  laiu  by  which  they  are  regulated  is  to 
understand  phenomena.  For  law  is  nothing  more  than 
the  general  conception  in  which  a  series  of  similarly 
recurring  natural  processes  may  be  embraced.  Just  as 
we  include  in  the  conception  '  mammal '  all  that  is  common 
to  the  man,  the  ape,  the  dog,  the  lion,  the  hare,  the  horse, 
the  whale,  &c.,  so  we  comprehend  in  the  law  of  refraction 
that  which  we  observe  to  regularly  recur  when  a  ray  of 
light  of  any  colour  passes  in  any  direction  through  the 
common  boimdary  of  any  two  transparent  media. 

A  law  of  nature,  however,  is  not  a  mere  logical  con- 
ception that  we  have  adopted  as  a  kind  of  memoria 
technica  to  enable  us  to  more  readily  remember  facts. 
We  of  the  present  day  have  already  sufficient  insight  to 
know  that  the  laws  of  nature  are  not  things  which  we  can 
evolve  by  any  speculative  method.  On  the  contrary,  we 
have  to  discover  them  in  the  facts ;  we  have  to  test  them 
by  repeated  observation  or  experiment,  in  constantly  new 
cases,  under  ever-varying  circumstances  ;  and  in  propor- 
tion only  as  they  hold  good  under  a  constantly  increasing 
change  of  conditions,  in  a  constantly  increasing  number 
of  cases  and  with  greater  delicacy  in  the  means  of  ob- 
servation, does  oui*  confidence  in  their  trustworthiness 
rise. 

Thus  the  laws  of  nature  occupy  the  position  of  a  power 
with  which  we  are  not  familiar,  not  to  be  arbitrarily 
selected  and  determined  in  our  minds,  as  one  might 
devise  various  systems  of  animals  and  plants  one  after 
another,  so  long  as  the  object  is  only  one  of  classification. 
Before  we  can  say  that  our  knowledge  of  any  one  law 
of  nature  is  complete,  we   must  see  that  it  holds  good 


AIM  AND   PROGRESS   OF   PHYSICAL   SCIENCE.      371 

without  exception^  and  make  this  the  test  of  its  correct- 
ness. If  we  can  be  assured  that  the  conditions  under 
which  the  law  operates  have  presented  themselves,  the 
result  must  ensue  without  arbitrariness,  without  choice, 
without  our  co-operation,  and  from  the  very  necessity 
which  regulates  the  things  of  the  external  world  as  well 
as  our  perception.  The  law  then  takes  the  form  of  an 
objective  power,  and  for  that  reason  we  call  it  force. 

For  instance,  we  regard  the  law  of  refraction  objectively 
as  a  refractive  force  in  transparent  substances ;  the  law  of 
chemical  affinity  as  the  elective  force  exhibited  by  dif- 
ferent bodies  towards  one  another.  In  the  same  way,  we 
speak  of  electrical  force  of  contact  of  metals,  of  a  force 
of  adhesion,  capillary  force,  and  so  on.  Under  these 
names  are  stated  objectively  laws  which  for  the  most  part 
comprise  small  series  of  natural  processes,  the  conditions 
of  which  are  somewhat  involved.  In  science  our  con- 
ceptions begin  in  this  way.  proceeding  to  generalizations 
from  a  number  of  well-established  special  laws.  We  must 
endeavour  to  eliminate  the  incidents  of  form  and  dis- 
tribution in  space  which  masses  under  investigation  may 
present  by  trying  to  find  from  the  phenomena  attending 
large  visible  masses  laws  for  the  operation  of  infinitely 
small  particles ;  or,  expressed  objectively,  by  resolving 
the  forces  of  composite  masses  into  the  forces  of  their 
smallest  elementary  particles.  But  precisely  in  this, 
the  simplest  form  of  expression  of  force — namely,  of 
mechanical  force  acting  on  a  point  of  the  mass — is  it 
especially  clear  that  force  is  only  the  law  of  action  ob- 
jectively expressed.  The  force  arising  from  the  presence 
of  such  and  such  bodies  is  equivalent  to  the  acceleration 
of  the  mass  on  which  it  operates  multiplied  by  this  mass. 
The  actual  meaning  of  such  an  equation  is  that  it  ex- 
presses the  following  law :  if  such  and  such  masses  are 
present  and  no  other,  such  and  such  acceleration  of  their 
17 


372     AIM   AND   PROGRESS   OF   PHYSICAL   SCIENCE. 

individual  points  occurs.  Its  actual  signification  may  be 
compared  with  the  facts  and  tested  by  them.  The  ab- 
stract conception  of  force  we  thus  introduce  implies 
moreover,  that  we  did  not  discover  this  law  at  random, 
that  it  is  an  essential  law  of  phenomena. 

Our  desire  to  coir^jprehend  natural  phenomena,  in  other 
words,  to  ascertain  their  laws,  thus  takes  another  form 
of  expression — that  is,  we  have  to  seek  out  the  forces 
which  are  the  causes  of  the  phenomena.  The  conformity 
to  law  in  nature  must  be  conceived  as  a  causal  connection 
the  moment  we  recognise  that  it  is  independent  of  our 
thouo'ht  and  will. 

If  then  we  direct  our  inquiry  to  the  progress  of  physical 
science  as  a  whole,  we  shall  have  to  judge  of  it  by  the 
measure  in  which  the  recognition  and  knowledge  of  a 
causative  connection  embracing  all  natural  phenomena 
has  advanced. 

On  looking  back  over  the  history  of  our  sciences,  the 
first  great  example  we  find  of  the  subjugation  of  a  wide 
mass  of  facts  to  a  comprehensive  law,  occurred  in  the  case 
of  theoretical  mechanics,  the  fundamental  conception  of 
which  was  first  clearly  propounded  by  Oalileo.  The 
question  then  was  to  find  the  general  propositions  that  to 
us  now  appear  so  self-evident,  that  all  substance  is  inert, 
and  that  the  magnitude  of  force  is  to  be  measured  not  by 
its  velocity,  but  by  changes  in  it.  At  first  the  operation 
of  a  continually  acting  force  could  only  be  represented  as 
a  series  of  small  impacts.  It  was  not  till  Leibnitz  and 
Newton,  by  the  discovery  of  the  differential  calculus,  had 
dispelled  the  ancient  darkness  which  enveloped  the  con- 
ception of  the  infinite,  and  had  clearly  established  the 
conception  of  the  Continuous  and  of  continuous  change, 
that  a  full  and  productive  application  of  the  newly-found 
mechanical  conceptions  made  any  progress.  The  most 
singular  and  most  splendid  instance  of  such  an   applica- 


AIM   AND    PEOGEESS   OF   PHYSICAL   SCIENCE.      373 

tion  was  in  regard  to  the  motion  of  the  planets,  and  I 
need  scarcely  remind  you  here  how  brilliant  an  example 
astronomy  has  been  for  the  development  of  the  other 
branches  of  science.  In  its  case,  by  the  theory  of  gravi- 
tation, a  vast  and  complex  mass  of  facts  were  first 
embraced  in  a  single  principle  of  great  simplicity,  and 
such  a  reconciliation  of  theory  and  fact  established  as 
has  never  been  accomplished  in  any  other  department  of 
science,  either  before  or  since.  In  supplying  the  wants  of 
astronomy,  have  originated  almost  all  the  exact  methods 
of  measurement  as  well  as  the  principal  advances  made 
in  modern  mathematics ;  the  science  itself  was  peculiarly 
fitted  to  attract  the  attention  of  the  general  public,  partly 
by  the  grandeur  of  the  objects  under  investigation,  partly 
by  its  practical  utility  in  navigation  and  geodesy,  and 
the  many  industrial  and  social  interests  arising  from 
them. 

Galileo  began  with  the  study  of  terrestrial  gravity. 
Newton  extended  the  application,  at  first  cautiously  and 
hesitatingly,  to  the  moon,  then  boldly  to  all  the  planets. 
And,  in  more  recent  times,  we  learn  that  these  laws  of  the 
common  inertia  and  gravitation  of  all  ponderable  masses 
hold  good  of  the  movements  of  the  most  distant  double 
stars  of  which  the  light  has  yet  reached  us. 

During  the  latter  half  of  the  last  and  the  first  half  of  the 
present  century  came  the  great  progress  of  chemistry 
which  conclusively  solved  the  ancient  problem  of  dis- 
covering the  elementary  substances,  a  task  to  which  so 
much  metaphysical  speculation  had  been  devoted.  Reality 
has  always  far  exceeded  even  the  boldest  and  wildest 
speculation,  and,  in  the  place  of  the  four  primitive  meta- 
physical elements — fire,  water,  air,  and  earth — we  have  now 
the  sixty-five  simple  bodies  of  modern  chemistry.  Science 
has  shown  that  these  elements  are  really  indestructible,  un- 
alterable in  their  mass,  unalterable  also  in  their  properties  j 


374     AIM  AIST)   PROGRESS   OF   PHYSICAL   SCIEx^CE. 

in  short,  that  from  every  condition  into  which  they  may 
have  been  converted^  they  can  invariably  be  isolated,  and 
recover  those  qualities  which  they  previously  possessed  in 
the  free  state.  Through  all  the  varied  phases  of  the 
phenomena  of  animated  and  inanimate  nature,  so  far  as 
we  are  acquainted  with  them,  in  all  the  astonishing  results 
of  chemical  decomposition  and  combination,  the  number 
and  diversity  of  which  the  chemist  with  unwearied  dili- 
gence augments  from  year  to  year,  the  one  law  of  the 
i immutability  of  matter  prevails  as  a  necessity  that  knows 
no  exception.  And  chemistry  has  already  pressed  on  into 
the  depths  of  immeasurable  space,  and  detected  in  the 
most  distant  suns  or  nebulae  indications  of  well-known 
terrestrial  elements,  so  that  doubts  respecting  the  pre- 
vailing homogeneity  of  the  matter  of  the  universe  no 
longer  exist,  though  certain  elements  may  perhaps  be 
restricted  to  certain  groups  of  the  heavenly  bodies. 

From  this  invariability  of  the  elements  follows  another 
and  wider  consequence.  Chemistry  shows  by  actual  experi- 
ment that  all  matter  is  made  up  of  the  elements  which 
have  been  already  isolated.  These  elements  may  exhibit 
great  differences  as  regards  combination  or  mixture,  the 
mode  of  ao^orecration  or  molecular  structure — that  is  to 
say,  they  may  vary  the  mode  of  their  distribution  in 
space.  In  their  'properties,  on  the  other  hand,  they  are 
altogether  unchangeable  ;  in  other  words,  when  referred 
to  the  same  compound,  as  regards  isolation,  and  to  the 
same  state  of  aggregation,  they  invariably  exhibit  the 
same  properties  as  before.  If,  then,  all  elementary  sub- 
stances are  unchangeable  in  respect  to  their  properties, 
and  only  changeable  as  regards  their  combination  and 
tlieir  states  of  aggregation — that  is,  in  respect  to  their 
distribution  in  space — it  follows  that  all  changes  in  the 
world  are  changes  in  the  local  distribution  of  elementary 
matter,  and  are  eventually  brought  about  through  Motion. 


AIM  AND   PKOGRESS   OF   PHYSICAL   SCIENCE.      375 

If,  however,  motion  be  the  primordial  change  which 
lies  at  the  root  of  all  the  other  changes  occurring  in  the 
world,  every  elementary  force  is  a  force  of  motion,  and  the 
ultimate  aim  of  physical  science  must  be  to  determine 
the  movements  which  are  the  real  causes  of  all  other 
phenomena  and  discover  the  motive  powers  on  which  they 
depend  ;  in  other  words,  to  merg'^  itself  into  mechanics. 

Though  this  is  clearly  the  final  consequence  of  the 
qualitative  and  quantitative  immutability  of  matter,  it  is 
after  all  an  ideal  proposition,  the  realization  of  which  is 
still  very  remote.  The  field  is  a  prescribed  one,  in  which 
we  have  succeeded  in  tracing  back  actually  observed 
changes  to  motions  and  forces  of  motion  of  a  definite 
kind.  Besides  astronomy,  may  be  mentioned  the  purely 
mechanical  part  of  physics,  then  acoustics,  optics,  and 
electricity ;  in  the  science  of  heat  and  in  chemistry, 
strenuous  endeavours  are  being  made  towards  perfecting 
definite  views  respecting  the  nature  of  the  motion  and 
position  of  molecules,  wliile  physiology  has  scarcely  made 
a  definite  step  in  this  direction. 

This  renders  all  the  more  important,  therefore,  a  note- 
worthy advancement  of  the  most  general  importance  made 
during  the  last  quarter  of  a  century  in  the  direction  we  are 
considering.  If  all  elementary  forces  are  forces  of  motion, 
and  all,  consequently,  of  similar  nature,  they  should  all 
be  measurable  by  the  same  standard,  that  is,  the  standard 
of  the  mechanical  forces.  And  that  this  is  actually  the 
fact  is  now  regarded  as  proved.  The  law  expressing  this 
is  known  under  the  name  of  the  law  of  the  Conservation 
of  Force. 

For  a  small  group  of  natural  phenomena  it  had  already 
been  pronounced  by  Newton,  then  more  definitely  and  in 
more  general  terms  by  D.  Bernouilli,  and  so  continued  of 
recognised  application  in  the  greater  part  of  the  then 
known  purely  mechanical  processes.     Certain  amplifica- 


376     AIM   AND   PROGRESS   OF   PHYSICAL   SCIENCE. 

tions  at  times  attracted  attention,  like  those  of  Rumford, 
Davy,  and  Montgolfier.  The  first,  however,  to  compass 
the  clear  and  distinct  idea  of  this  law,  and  to  venture  to 
pronounce  its  absolute  universality,  was  one  whom  we 
shall  have  soon  the  pleasure  of  hearing  from  this  platform, 
Dr.  Robert  Mayer,  of  Heilbronn.  While  Dr.  Mayer  was 
led  by  physiological  questions  to  the  discovery  of  -the 
most  general  form  of  this  law,  technical  questions  in 
mechanical  engineering  led  Mr.  Joule,  of  Manchester, 
simultaneously,  and  independently  of  him,  to  the  same 
considerations  ;  and  it  is  to  Mr.  Joule  that  we  are  indebted 
for  those  important  and  laborious  experimental  researches 
in  that  department  where  the  applicability  of  the  law  of 
the  conservation  of  force  appeared  most  doubtful,  and 
where  the  greatest  gaps  in  actual  knowledge  occurred, 
namely,  in  the  production  of  work  from  heat,  and  of  heat 
from  work. 

To  state  the  law  clearly  it  was  necessary,  in  con- 
tradistinction to  Galileo's  conception  of  the  intensity 
of  force,  that  a  new  mechanical  idea  was  elaborated, 
which  we  may  term  the  conception  of  the  quantity  of 
force,  and  which  has  also  been  called  quantity  of  work 
or  of  energy* 

A  way  to  this  conception  of  the  quantity  of  force  had 
been  prepared  partly,  in  theoretical  mechanics,  through 
the  conception  of  the  amount  of  vis  viva  of  a  moving 
body,  and  partly  by  practical  mechanics  through  the 
conception  of  the  motive  power  necessary  to  keep  a 
machine  at  work.  Practical  machinists  had  already 
found  a  standard  by  which  any  motive  power  could  be 
measured,  in  the  determination  of  the  number  of  pounds 
that  it  could  lift  one  foot  in  a  second ;  and,  as  is  known, 
a  horse-power  was  defined  to  be  equivalent  to  the  motive 
power  required  to  lift  seventy  kilogrammes  one  metre  in 
each  second. 


AIM   AND   PROGRESS   OF   PHYSICAL   SCIENCE.      377 

Machines,  and  the  motive  powers  required  for  their 
movement,  furnish,  in  fact,  the  most  familiar  illustra- 
tions of  the  uniformity  of  all  natural  forces  expressed  by 
the  law  of  the  conservation  of  force.  Any  machine  which 
is  to  be  set  in  motion  requires  a  mechanical  motive 
power.  Whence  this  power  is  derived  or  what  its  form, 
is  of  no  consequence,  provided  only  it  be  sufficiently 
great  and  act  continuously.  At  one  time  we  employ  a 
steam-engine,  at  another  a  water-wheel  or  turbine,  here 
horses  or  oxen  at  a  whim,  there  a  windmill,  or  if  but 
little  power  is  required,  the  human  arm,  a  raised  weight, 
or  an  electro-magnetic  engine.  The  choice  of  the  machine 
is  merely  dependent  on  the  amount  of  power  we  would 
use,  or  the  force  of  circumstance.  In  the  watermill  the 
weight  of  the  water  flowing  down  the  hills  is  the  agent ; 
it  is  lifted  to  the  hills  by  a  meteorological  process,  and 
becomes  the  source  of  motive  power  for  the  mill.  In  the 
windmill  it  is  the  vis  viva  of  the  moving  air  which 
drives  round  the  sails ;  this  motion  also  is  due  to  a 
meteorological  operation  of  the  atmosphere.  In  the  steam- 
engine -we  have  the  tension  of  the  heated  vapour  which 
drives  the  piston  to  and  fro ;  this  is  engendered  by  the 
heat  arising  from  the  combustion  of  the  coal  in  the  tire- 
box,  in  other  words,  by  a  chemical  process  ;  and  in  this 
case  the  latter  action  is  the  source  of  the  motive  power. 
If  it  be  a  horse  or  the  human  arm  which  is  at  work,  we 
have  the  muscles  stimulated  through  the  nerves,  directly 
producing  the  mechanical  force.  In  order,  however,  that 
the  living  body  may  generate  muscular  power  it  must  be 
nourished  and  breathe.  The  food  it  takes  separates  again 
from  it,  after  having  combined  with  the  oxygen  inhaled 
from  the  air,  to  form  carbonic  acid  and  water.  Here 
again,  then,  a  chemical  process  is  an  essential  element  to 
maintain  muscular  power.  A  similar  state  of  things  is  ob- 
served in  the  electro-magnetic  machines  of  our  telegraphs. 


378     AIM   AND   PEOGRESS    OF   PHYSICAL   SCIENCE. 

Thus,  then,  we  obtain  mechanical  motive  force  from 
the  most  varied  processes  of  nature  in  the  most  different 
ways:  but  it  will  also  be  remarked  in  only  a  limited 
quantity.  In  doing  so  we  always  consuTne  something  that 
nature  supplies  to  us.  In  the  watermill  we  use  a  quantity 
of  water  collected  at  an  elevation,  coal  in  the  steam- 
engine,  zinc  and  sulphuric  acid  in  the  electro-magnetic 
machine,  food  for  the  horse ;  in  the  windmill  we  use  up 
the  motion  of  the  wind,  which  is  arrested  by  the  sails. 

Conversely,  if  we  have  a  motive  force  at  our  disposal 
we  can  develop  with  it  forms  of  action  of  the  most  varied 
kind.  It  will  not  be  necessary  in  this  place  to  enumerate 
the  countless  diversity  of  industrial  machines,  and  the 
varieties  of  work  which  they  perform. 

Let  us  rather  consider  the  physical  differences  of  the 
possible  performance  of  a  motive  power.  With  its  help 
we  can  raise  loads,  pump  water  to  an  elevation,  compress 
gases,  set  a  railway  train  in  motion,  and  through  friction 
generate  heat.  By  its  aid  we  can  turn  magneto-electric 
machines,  and  produce  electric  currents,  and  with  them 
decompose  water  and  other  chemical  compounds  having 
the  most  powerful  affinities,  render  wires  incandescent, 
magnetise  iron^  &c. 

Moreover,  had  we  at  our  disposal  a  sufficient  me- 
chanical motive  force  we  could  lestore  all  those  states 
and  conditions  from  which,  as  was  seen  above,  we  are 
enabled  at  the  outset  to  derive  mechanical  motive  power. 

As,  however,  the  motive  power  derived  from  any 
given  natural  process  is  limited,  so  likewise  is  there  a 
limitation  to  the  total  amount  of  modifications  which  we 
may  produce  by  the  use  of  any  given  motive  power. 

These  deductions,  arrived  at  first  in  isolated  instances 
from  machines  and  physical  apparatus,  have  now  been 
welded  into  a  law  of  nature  of  the  widest  validity.  Every 
change  in  nature  is  equivalent  to  a  certain  development. 


AIM  AND   PROGRESS   OP   PHYSICAL   SCIENCE.     379 

or  a  certain  consumption  of  motive  force.  If  motive 
power  be  developed  it  may  either  appear  as  such,  or  be 
directly  used  up  again  to  form  other  changes  equivalent 
in  magnitude.  The  leading  determinations  of  this  equiva- 
lency are  founded  on  Joule's  measurements  of  the  me- 
chanical equivalent  of  heat.  When,  by  the  application 
of  heat,  we  set  a  .«5team-engine  in  motion,  heat  propor- 
tional to  the  work  done  disappears  within  it;  in  short, 
the  heat  which  can  warm  a  given  weight  of  water  one 
degree  of  the  Centigrade  scale  is  able,  if  converted  into 
work,  to  lift  the  same  weight  of  water  to  a  height  of 
425  metres.  If  we  convert  work  into  heat  by  friction 
we  again  use,  in  heating  a  given  weight  of  water  one 
degree  Centigrade,  the  motive  force  which  the  same 
quantity  of  water  would  have  generated  in  flowing  down 
from  a  height  of  425  metres.  Chemical  processes  gene- 
rate heat  in  definite  proportion,  and  in  like  manner  we 
estimate  the  motive  power  equivalent  to  such  chemical 
forces;  and  thus  the  energy  of  the  chemical  force  of 
affinity  is  also  measurable  by  the  mechanical  standard. 
The  same  holds  true  for  all  the  other  forms  of  natural 
forces,  but  it  will  not  be  necessary  to  pursue  the  subject 
further  here. 

It  has  actually  been  established,  then,  as  a  result  of 
these  investigations,  that  all  the  forces  of  nature  are 
measurable  by  the  same  mechanical  standard,  and  that 
all  pure  motive  forces  are,  as  regards  performance  of 
work,  equivalent.  And  thus  one  great  step  towards  the 
solution  of  the  comprehensive  theoretical  task  of  referring 
all  natural  phenomena  to  motion  has  been  accomplished. 

Whilst  the  foregoing  considerations  chiefly  seek  to 
elucidate  the  logical  value  of  the  law  of  the  conservation 
of  force,  its  actual  signification  in  the  general  conception 
of  the  processes  of  nature  is  expressed  in  the  grand  con- 
nection which  it  establishes  between  the  entire  processes 


380     AIM  AND   PHOGRESS   OF   PHYSICAL   SCIEXCE. 

of  the  universe,  through  all  distances  of  place  or  time. 
The  universe  appears,  according  to  this  law,  to  be  en- 
dowed with  a  store  of  energy  which,  through  all  the 
varied  changes  in  natural  processes,  can  neither  be 
increased  nor  diminished,  which  is  maintained  therein 
in  ever-varying  phases,  but,  like  matter  itself,  is  from 
eternity  to  eternity  of  unchanging  magnitude ;  acting 
in  space^  but  not  divisible^  as  matter  is,  with  it.  Every 
change  in  the  world  simply  consists  in  a  variation  in  the 
mode  of  appearance  of  this  store  of  energy.  Here  we 
find  one  portion  of  it  as  the  vis  viva  of  moving  bodies, 
there  as  regular  oscillation  in  light  and  sound  ;  or,  again, 
as  heat,  that  is  to  say,  the  irregular  motion  of  invisible 
particles  ;  at  another  point  the  energy  appears  in  the 
form  of  the  weight  of  two  masses  gravitating  towards 
each  other,  then  as  internal  tension  and  pressure  of 
elastic  bodies,  or  as  chemical  attraction,  electrical  ten- 
sion, or  magnetic  distribution.  If  it  disappear  in  one 
form,  it  reappears  as  surely  in  another ;  and  whenever 
it  presents  itself  in  a  new  phase  we  are  certain  that 
it  does  so  at  the  expense  of  one  of  its  other  forms. 

Carnot's  law  of  tlie  mechanical  theory  of  heat,  as 
modified  by  Clausius,  has,  in  fact,  made  it  clear  that 
this  change  moves  in  the  main  continuously  onward  in  a 
definite  direction,  so  that  a  constantly  increasing  amount 
of  the  great  store  of  energy  in  the  universe  is  being 
transformed  into  heat. 

We  can,  therefore,  see  with  the  mind's  eye  the  original 
condition  of  things  in  which  the  matter  composing  the 
celestial  bodies  was  still  cold,  and  probably  distributed 
as  chaotic  vapour  or  dust  through  space  ;  we  see  that 
it  must  have  developed  heat  when  it  collected  together 
under  the  influence  of  gravity.  Even  at  the  present 
time  spectrum  analysis  (a  method  the  theoretical  prin- 
ciples of  which  owe  their  origin  to  the  mechanical  theory 


AIM   AND    PROGHESS   OP   PHYSICAL   SCIENCE.      381 

of  heat)  enables  us  to  detect  remains  of  this  loosely- 
distributed  naatter  in  the  nebulae  ;  we  recognise  it  in  the 
meteor-showers  and  comets  ;  the  act  of  agglomeration 
and  the  development  of  heat  still  continue,  though  in 
our  portion  of  the  stellar  system  they  have  ceased  to 
a  great  extent.  The  chief  part  of  the  primordial 
energy  of  the  matter  belonging  to  our  system  is  now 
in  the  form  of  solar  heat.  This  energy,  however,  will 
not  remain  locked  up  in  our  system  for  ever :  portions 
of  it  are  continually  radiating  from  it,  in  the  form  of 
light  and  heat,  into  infinite  space.  Of  this  radiation 
our  earth  receives  a  share.  It  is  these  solar  heat-rays 
which  produce  on  the  earth's  surface  the  winds  and  the 
currents  of  the  ocean,  and  lift  the  watery  vapour  from 
the  tropical  seas,  which,  distilling  over  hill  and  plain, 
returns  as  springs  and  rivers  to  the  sea.  The  solar  rays 
impart  to  the  plant  the  power  to  separate  from  carbonic 
acid  and  water  those  combustible  substances  which  serve 
as  food  for  animals,  and  thus,  in  even  the  varied  changes 
of  organic  life,  the  moving  power  is  derived  from  the 
infinitely  vast  store  of  the  universe. 

This  exalted  picture  of  the  connection  existing  between 
all  the  processes  of  nature  has  been  often  presented  to 
us  in  recent  times  ;  it  will  suffice  here  that  I  direct 
attention  to  its  leading  features.  If  the  task  of  physical 
science  be  to  determine  laws,  a  step  of  the  most  com- 
prehensive significance  towards  that  object  has  here  been 
taken. 

The  application  of  the  law  of  the  conservation  of  force 
to  the  vital  processes  of  animals  and  plants,  which  has 
just  been  discussed,  leads  us  in  another  direction  in 
which  our  knowledge  of  nature's  conformity  to  law  has 
made  an  advance.  The  law  to  which  we  referred  is 
of  the  most  essential  importance  in  leading  questions 
of  physiology,  and  it  was  for  this  reason  that  Dr.  Mayer 


382     AIM   AND   PROGRESS    OF   PHYSICAL   SCIEXCE 

and  I  were  led  on  physiological  grounds  to  investigations 
having  especial  reference  to  the  conservation  of  force. 

As  regards  the  phenomena  of  inorganic  nature  all 
doubts  have  long  since  been  laid  to  rest  respecting  the 
principles  of  the  method.  It  was  apparent  that  these 
phenomena  had  fixed  laws,  and  examples  enough  were 
already  known  to  make  the  finding  of  such  laws  probable. 

In  consequence,  however,  of  the  greater  complexity  of 
the  vital  processes,  their  connection  with  mental  action, 
and  the  unmistakable  evidence  of  adaptability  to  a  pur- 
pose which  organic  structures  exhibit,  the  existence  of  a 
settled  conformity  to  law  might  well  appear  doubtful,  and, 
in  fact,  physiology  has  always  had  to  encounter  this 
fundamental  question  :  are  all  vital  processes  absolutely 
conformable  to  law  ?  Or  is  there,  perhaps,  a  range  of 
greater  or  less  magnitude  within  which  an  exception 
prevails  r  More  or  less  obscured  by  words,  the  view  of 
Paracelsus,  Helmont,  and  Stahl,  has  been,  and  is  at 
present,  held,  particulaily  outside  Germany,  that  there 
exists  a  soul  of  life  {''  Lebensseele")  directing  the  organic 
processes  which  is  endowed  more  or  less  with  conscious- 
ness like  the  soul  of  man.  The  influence  of  the  inorganic 
forces  of  nature  on  the  organism  was  still  recognised 
on  the  assumption  that  the  soul  of  life  only  exercises 
power  over  matter  by  means  of  the  physical  and  chemical 
forces  of  matter  itself;  so  that  without  this  aid  it  could 
accomplish  nothing,  but  that  it  possessed  the  faculty  of 
suspending  or  permitting  the  operation  of  the  forces 
at  pleasure. 

After  death,  when  no  longer  subject  to  the  control  of 
the  soul  of  life  or  vital  force,  it  was  these  very  chemical 
forces  of  organic  matter  which  brought  about  decomposi- 
tion. In  short,  through  all  the  different  modes  of  ex- 
pressing it,  whether  it  was  termed  the  Archaus,  the 
anima  inscia,  or  the   vital  force  and   the   restorative 


AIM  AND   PROGRESS   OF   PHYSICAL   SCIENCE.     383 

'power  of  nature^  the  faculty  to  build  up  the  body  accord- 
ing to  system,  and  to  suitably  accommodate  it  to  external 
circumstances,  remained  the  most  essential  attribute  of 
this  hypothetically  controlling  principle  of  the  vitalistic 
theory  with  which,  therefore,  by  reason  of  its  attributes, 
only  the  name  of  soul  fully  harmonised. 

It  is  apparent,  however,  that  this  notion  runs  directly 
counter  to  the  law  of  the  conservation  of  force.  If  vital 
force  were  for  a  time  to  annul  the  gravity  of  a  weight, 
it  could  be  raised  without  labour  to  any  desired  height, 
and  subsequently,  if  the  action  of  gravity  were  again 
restored,  could  perform  work  of  any  desired  magnitude. 
And  thus  work  could  be  obtained  out  of  nothing  without 
expense.  If  vital  force  could  for  a  time  suspend  the 
chemical  affinity  of  carbon  for  oxygen,  carbonic  acid 
could  be  decomposed  without  work  being  employed  for 
that  purpose,  and  the  liberated  carbon  and  oxygen 
could  perform  new  work. 

In  reality,  however,  no  trace  of  such  an  action  is  to 
be  met  with  as  that  of  the  living  organism  being  able 
to  generate  an  amount  of  work  without  an  equivalent 
expenditure.  When  we  consider  the  work  done  by 
animals,  we  find  the  operation  comparable  in  every 
respect  with  that  of  the  steam-engine.  Animals,  like 
machines,  can  only  move  and  accomplish  work  by  being 
continuously  supplied  with  fuel  (that  is  to  say,  food)  and 
air  containing  oxygen  ;  both  give  off  again  this  material 
in  a  burnt  state,  and  at  the  same  time  produce  heat  and 
work.  All  investigation,  thus  far,  respecting  the  amoimt 
of  heat  which  an  animal  produces  when  at  rest  is  in 
no  way  at  variance  with  the  assumption  that  this  heat 
exactly  corresponds  to  the  equivalent,  expressed  as  work, 
of  the  forces  of  chemical  affinity  then  in  action. 

As  regards  the  work  done  by  plants,  a  source  of  power 
in  every  way  sufficient,  exists  in  the  solar  rays  which  they 


384     AIM  AKB   PROGRESS   OF   PHYSICAL   SCIENCE. 

require  for  the  increase  of  the  organic  naatter  of  their 
structures.  Meanwhile  it  is  true  that  exact  quantitative 
determinations  of  the  equivalents  of  force,  consumed  and 
produced  in  the  vegetable  as  well  as  the  animal  kingdom, 
have  still  to  be  made  in  order  to  fully  establish  the 
exact  accordance  of  these  two  values. 

If,  then,  the  law  of  the  conservation  of  force  hold 
good  also  for  the  living  body,  it  follows  that  the  physical 
and  chemical  forces  of  the  material  employed  in  building 
up  the  body  are  in  continuous  action  without  inter- 
mission and  without  choice,  and  that  their  exact  con- 
formity to  law  never  suffers  a  momenfs  interruption. 

Physiologists,  then,  must  expect  to  meet  with  an  un- 
conditional conformity  to  law  of  the  forces  of  nature 
in  their  inquiries  respecting  the  vital  processes ;  they 
will  have  to  apply  themselves  to  the  investigation  of  the 
physical  and  chemical  processes  going  on  within  the 
organism.  It  is  a  task  of  vast  complexity  and  extent ; 
but  the  workers,  in  Germany  especially,  are  both  nu- 
merous and  enthusiastic,  and  we  may  already  affirm 
that  their  labours  have  not  been  unrewarded,  inasmuch 
as  our  knowledge  of  the  vital  phenomena  has  made 
greater  progress  during  the  last  forty  years  than  in  the 
two  preceding  centuries. 

Assistance,  that  cannot  be  too  highly  valued,  towards 
the  elucidation  of  the  fundamental  principles  of  the 
doctrine  of  life,  has  been  rendered  on  the  part  of  descrip- 
tive natural  history,  through  Darwin's  theory  of  the 
evolution  of  organic  forms,  by  which  the  possibility  of 
an  entirely  new  interpretation  of  organic  adaptability  is 
furnished. 

The  adaptability  in  the  construction  of  the  functions 
of  the  living  body,  most  wonderful  at  any  time,  and 
with  the  progress  of  science  becoming  still  more  so,  was 
doubtless  the  chief  reason   that  provoked  a  comparison 


AIM  AND   PROGHESS   OP   PHYSICAL   SCIENCE.     385 

of  the  vital  processes  with  the  actions  of  a  principle 
actino:  like  a  soul.  In  the  whole  external  world  we  know 
of  but  one  series  of  phenomena  possessing  similar 
characteristics,  we  mean  the  actions  and  deeds  of  an 
intelligent  human  being  ;  and  we  must  allow  that  in 
innumerable  instances  the  organic  adaptability  appears  to 
be  so  extraordinarily  superior  to  the  capacities  of  the 
human  intelligence  that  we  might  feel  disposed  to  ascribe 
to  it  a  higher  rather  than  a  lower  character. 

Before  the  time  of  Darwin  only  two  theories  respect- 
ing organic  adaptability  were  in  vogue,  both  of  which 
pointed  to  the  interference  of  free  intelligence  in  the 
course  of  natural  processes.  On  the  one  hand  it  was 
held,  in  accordance  with  the  vitalistic  theory,  that  the 
vital  processes  were  continuously  directed  by  a  living 
soul ;  or,  on  the  other,  recourse  was  had  to  an  act  of 
supernatural  intelligence  to  account  for  the  origin  of 
every  living  species.  The  latter  view  indeed  supposes 
that  the  causal  connection  of  natural  phenomena  had  been 
broken  less  often,  and  allows  of  a  strict  scientific  examina- 
tion of  the  processes  observable  in  the  species  of  human 
beings  now  existing  ;  but  even  it  is  not  able  to  entirely 
explain  away  those  exceptions  to  the  law  of  causality, 
and  consequently  it  enjoyed  no  considerable  favour  as 
opposed  to  the  vitalistic  view,  which  was  powerfully 
supported,  by  apparent  evidence,  that  is,  by  the  natural 
desire  to  find  similar  causes  behind  similar  phenomena. 

Darwin's  theory  contains  an  essentially  new  creative 
thought.  It  shows  how  adaptability  of  structure  in 
organisms  can  result  from  a  blind  rule  of  a  law 
of  natiu'e  without  any  intervention  of  intelligence.  I 
allude  to  the  law  of  transmission  of  individual  pecu- 
liarities from  parent  to  offspring,  a  law  long  known 
and  recognised,  and  only  needing  a  «iore  precise  defi- 
nition.     If  both   parents  have   individual   peculiarities 


386     AIM  AXD   PROGRESS   OF   PHYSICAL   SCIENCE. 

in  common,  the  majority  of  their  offspring  also  possess 
them  ;  and  if  among  the  offspring  there  are  some  which 
present  these  peculiarities  in  a  less  marked  degree,  there 
will,  on  the  other  hand,  always  be  found  among  a  great 
number,  others  in  which  the  same  peculiarities  have 
become  intensified.  If,  now,  these  be  selected  to  propa- 
gate offspring,  a  greater  and  greater  intensification  of 
these  peculiarities  may  be  attained  and  transmitted. 
This  is,  in  fact,  the  method  employed  in  cattle-breeding 
and  gardening,  in  order  with  greater  certainty  to  obtain 
new  breeds  and  varieties,  with  well-marked  different 
characters.  The  experience  of  artificial  breeding  is  to 
be  regarded,  from  a  scientific  point  of  view,  as  an  ex- 
perimental confirmation  of  the  law  imder  discussion ; 
and,  in  fact,  this  experiment  has  proved  successful,  and 
is  still  doing  so,  with  species  of  every  class  of  the  animal 
kingdom,  and,  with  respect  to  tlie  most  different  organs 
of  the  body,  in  a  vast  number  of  instances. 

After  the  general  application  of  the  law  of  trans- 
mission had  been  established  in  this  way,  it  only  re- 
mained for  Darwin  to  discuss  the  bearings  of  the  question 
as  regards  animals  and  plants  in  the  wild  state.  The 
result  which  has  been  arrived  at  is  that  those  inaividuals 
whicli  are  distinguished  in  the  struggle  for  existence 
by  some  advantageous  quality,  are  the  most  likely  to 
produce  offspring,  and  thus  transmit  to  them  their  ad- 
vantageous qualities.  And  in  this  way  from  generation 
to  generation  a  gradual  adjustment  is  arrived  at  in  the 
adaptation  of  each  species  of  living  creation  to  the 
conditions  under  which  it  has  to  live  until  the  type 
has  reached  such  a  degree  of  perfection  that  any  sub- 
stantial variation  from  it  is  a  disadvantage.  It  will 
then  remain  unchanged  so  long  as  the  external  con- 
ditions of  its  existence  remain  materially  unaltered. 
Such   an   ala^ost   absolutely  fixed  condition   appears  to 


AIM  AND   PROGRESS   OF   PHYSICAL   SCIENCE.      387 

be  attained  by  the  plants  and  animals  now  living,  and 
thus  the  continuity  of  the  species,  at  least  during 
historic  times,  is  found  to  prevail. 

An  animated  controversy,  however,  still  continues,  con- 
cerning the  truth  or  probability  of  tlie  Darwinian  theory, 
for  the  most  part  respecting  the  limits  that  should  be 
assigned  to  the  variation  of  species.  The  opponents  of 
this  view  would  hardly  deny  that,  as  assumed  by  Darwin, 
hereditary  differences  of  race  could  have  arisen  in  one 
and  the  same  species  ;  or,  in  other  words,  that  many  of 
the  forms  hitherto  regarded  as  distinct  species  of  the  same 
genus  have  been  derived  from  the  same  primitive  form. 
Whether  we  must  restrict  our  view  to  this,  or  whether, 
perhaps,  we  venture  to  derive  all  mammals  from  one  origi- 
nal marsupial,  or,  again,  all  vertebrates  from  a  primitive 
lancelet,  or  all  plants  and  animals  together  from  the  slimy 
protoplasm  of  a  protiston,  depends  at  the  present  moment 
rather  on  the  leanings  of  individual  observers  than  on 
facts.  Fresh  links,  connecting  classes  of  apparently 
irreconcilable  type,  are  always  presenting  themselves ; 
the  actual  transition  of  forms,  into  others  widely  different, 
has  already  been  traced  in  regularly  deposited  geological 
strata,  and  has  come  to  be  beyond  question ;  and  since 
this  line  of  research  has  been  taken  up,  how  numerous 
are  the  facts  which  fully  accord  with  Darwin's  theory, 
and  give  special  effect  to  it  in  detail ! 

At  the  same  time,  we  should  not  forget  the  clear  in- 
terpretation Darwin's  grand  conception  has  supplied  of 
the  till  then  mysterious  notions  respecting  natural  affinity, 
natural  systems,  and  homology  of  organs  in  various 
animals  ;  how  by  its  aid  the  remarkable  recurrence  of 
the  structural  peculiarities  of  lower  animals  in  the 
embryos  of  others  higher  in  the  scale,  the  special  kind 
of  development  appearing  in  the  series  of  palseontological 
forms,  and  the  peculiar  conditions  of  affinity  of  the  faunas 


388     AIM   AND   PROGRESS   OF   PHYSICAL   SCIENCE. 

and  floras  of  limited  areas  have,  one  and  all,  received 
elucidation.  Formerly  natural  affinity  appeared  to  be  a 
mere  enigmatical,  and  altogether  groimdless  similarity 
of  forms ;  now  it  has  become  a  matter  for  actual  consan- 
guinity. The  natural  system  certainly  forced  itself  as 
such  upon  the  mind,  although  theory  strictly  disavowed 
any  real  significance  to  it;  at  present  it  denotes  an 
actual  genealogy  of  organisms.  The  facts  of  palaeonto- 
logical  and  embryological  evolution  and  of  geographical 
distribution  were  enigmatical  wonders  so  long  as  each 
species  was  regarded  as  the  result  of  an  independent  act 
of  creation,  and  cast  a  scarcely  favourable  light  on  the 
strange  tentative  method  which  was  ascribed  to  the 
Creator.  Darwin  has  raised  all  these  isolated  questions 
from  the  condition  of  a  heap  of  enigmatical  wonders 
to  a  great  consistent  system  of  development,  and  esta- 
blished definite  ideas  in  the  place  of  such  a  fanciful 
hypothesis  as,  among  the  first,  had  occurred  to  Groethe, 
respecting  the  facts  of  the  comparative  anatomy  and  the 
morphology  of  plants. 

This  renders  possible  a  definite  statement  of  problems 
for  further  inquiry,  a  great  gain  in  any  case,  even  should 
it  happen  that  Darwin's  theory  does  not  embrace  the  whole 
truth,  and  that,  in  addition  to  the  influences  which  he  has 
indicated,  there  should  be  found  to  be  others  which 
operate  in  the  modification  of  organic  forms. 

While  the  Darwinian  theory  treats  exclusively  of  the 
gradual  modification  of  species  after  a  succession  of 
generations,  we  know  that  a  single  individual  may  adapt 
itself,  or  become  accustomed,  in  a  certain  degree,  to  the 
circumstances  under  which  it  has  to  live  ;  and  that  even 
during  the  single  life  of  an  individual  a  distinct  progress 
towards  a  higher  development  of  organic  adaptability 
may  be  attained.  And  it  is  more  especially  in  those 
forms  of  organic  life  where  the  adaptability  in  structure 


AIM   AND    PEOGRESS   OF   PHYSICAL   SCIENCE.      389 

has  reached  the  highest  grade  and  excited  the  greatest 
admiration,  namely,  in  the  region  of  mental  perception, 
that,  as  the  latest  results  of  physiology  teach  us,  this 
individual  adaptation  plays  a  most  prominent  part. 

Who  has  not  marvelled  at  the  fidelity  and  accuracy 
of  the  information  which  our  senses  convey  to  us  from 
the  surrounding  world,  more  especially  those  of  the  far- 
reaching  eye  ?  The  information  so  gained  furnishes  the 
premisses  for  the  conclusions  which  we  come  to,  the  acts 
that  we  perform ;  and  unless  our  senses  convey  to  us 
correct  impressions,  we  cannot  expect  to  act  accurately, 
so  that  results  shall  correspond  with  our  expectations. 
By  the  success  or  failure  of  our  acts  we  again  and  again 
test  the  truth  of  the  information  with  which  our  senses 
supply  us,  and  experience,  after  millions  of  repetitions, 
shows  us  that  this  fidelity  is  exceedingly  great,  in  fact, 
almost  free  from  exceptions.  At  all  events,  these  exceptions, 
the  so-called  illusions  of  the  senses,  are  rare,  and  are  only 
brought  about  by  very  special  and  unusual  circumstances. 

Whenever  we  stretch  forth  the  hand  to  lay  hold  of 
something,  or  advance  the  foot  to  step  upon  some  object, 
we  must  first  form  an  accurate  optical  image  of  the  position 
of  the  object  to  be  touched,  its  form,  distance,  &c.,  or  we 
shall  fail.  The  certainty  and  accuracy  of  our  perception 
by  the  senses  must  at  least  equal  the  certainty  and 
accuracy  which  our  actions  have  attained  after  long 
practice  ;  and  the  belief,  therefore,  in  the  trustworthiness 
of  our  senses  is  no  blind  belief,  but  one,  the  accuracy  of 
which  has  been  tested  and  verified  again  and  again  by 
numberless  experiments. 

Were  this  harmony  between  the  perceptions  through 
the  senses  and  the  objects  causing  them,  in  other  words, 
this  basis  of  all  our  knowledge,  a  direct  product  of  the 
vital  principle,  its  formative  power  would,  in  fact,  then 
have  attained  the  highest  degree  of  perfection.     But  an 


390     AIM  AND   PROGRESS    OF   PHYSICAL   SCIENCE. 

examination  of  the  actual  facts  at  once  destroys  in  the 
most  merciless  manner  all  belief  in  a  preordained  harmony 
of  the  inner  and  external  world. 

I  need  not  call  to  mind  the  startling  and  unexpected  re- 
sults of  ophthalmometrical  and  optical  research  which  have 
proved  the  eye  to  be  a  by  no  means  more  perfect  optical 
instrument  than  those  constructed  by  human  hands  ;  but, 
on  the  contrary,  to  exhibit,  in  addition  to  the  faults 
inseparable  from  any  dioptric  instrument,  others  that  in 
an  artificial  instrument  we  should  severely  condemn  ;  nor 
need  I  remind  you  that  the  ear  conveys  to  us  sounds  from 
without  in  no  wise  in  the  ratio  of  their  actual  intensity, 
but  strangely  resolves  them  and  modifies  them,  intensify- 
ing or  weakening  them  in  very  different  degrees,  ac- 
cording to  their  varieties  of  pitch. 

These  anomalies,  however,  are  as  nothing  compared 
with  those  to  be  met  with  in  examining  the  nature  of  the 
sensations  by  which  we  become  acquainted  with  the 
various  properties  of  the  objects  surrounding  us.  Here 
it  can  at  once  be  proved  that  no  kind  and  no  degree  of 
similarity  exists  between  the  quality  of  a  sensation  and 
the  quality  of  the  agent  inducing  it,  and  portrayed  by  it. 

In  its  leading  features  this  was  demonstrated  by  Johannes 
Miiller  in  his  law  of  the  Specific  Action  of  the  Senses.  Ac- 
cording to  him,  each  nerve  of  sense  possesses  a  peculiar  kind 
of  sensation.  A  nerve,  we  know,  can  be  rendered  active 
by  a  vast  number  of  exciting  agents,  and  the  same  agent 
may  likewise  affect  different  organs  of  sense  ;  but  however 
it  be  brought  about,  we  never  have  in  nerves  of  sight 
any  other  sensation  than  that  of  light ;  in  the  nerves  of 
the  ear  any  other  than  a  sensation  of  sound ;  in  short, 
in  each  individual  nerve  of  sense  only  that  sensation 
which  corresponds  to  its  peculiar  specific  action.  The 
most  marked  differences  in  the  qualities  of  sensation, 
in  other  words,  those  between  the  sensations  of  different 


AIM   AND   PROGKESS   OF   PHYSICAL   SCIENCE.      391 

senses,  are,  then,  in  no  way  dependent  on  the  nature  of 
the  exciting  agent,  but  only  on  that  of  the  nerve  appa- 
ratus under  operation. 

The  bearing  of  Miiller's  law  has  been  extended  by 
later  research.  It  appears  highly  probable  that  even  the 
sensations  of  different  colours  and  different  pitch,  as  well 
as  qualitative  pf^culiarities  of  luminous  sensations  inter  se, 
and  of  sonorous  sensations  inter  se,  also  depend  on  the 
excitation  of  systems  of  fibres,  with  distinct  character 
and  endowed  with  different  specific  energy,  of  nerves 
of  sight  and  hearing  respectively.  The  infinitely  more 
varied  diversity  of  composite  light  is  in  this  way  refer- 
able to  sensations  of  only  threefold  heterogeneous 
character,  in  other  words,  to  mixtures  of  the  three 
primary  colours.  From  this  reduction  in  the  number  of 
possible  differences  it  follows  that  very  different  compo- 
site light  may  appear  the  same.  In  this  case  it  has  been 
shown  tliat  no  kind  of  physical  similarity  whatever  corre- 
sponds to  the  subjective  similarity  of  different  composite 
light  of  the  same  colour.  By  these  and  similar  facts  we  are 
led  to  the  very  important  conclusion  that  our  sensations 
are,  as  regards  their  quality,  only  sigiis  of  external 
objects,  and  in  no  sense  images  of  any  degree  of  re- 
semblance. An  image  must,  in  certain  respects,  be 
analogous  to  the  original  object ;  a  statue,  for  instance, 
has  the  same  corporeal  form  as  the  human  being  after 
which  it  is  made  ;  a  picture  the  same  colour  and  per- 
spective projection.  For  a  sign  it  is  sufficient  that  it 
become  apparent  as  often  as  the  occurrence  to  be  de- 
picted makes  its  appearance,  the  conformity  between 
them  being  restricted  to  their  presenting  themselves 
simultaneously ;  and  the  correspondence  existing  between 
our  sensations  and  the  objects  producing  them  is  pre- 
cisely of  this  kind.  They  are  signs  which  we  have 
learned  to  decipher,  and  a  language  given  us  with  our 


392     AIM   AND   PROGRESS   OF   PHYSICAL   SCIENCE. 

organisation  by  which  external  objects  discourse  to  us — 
a  language,  however,  like  our  mother  tongue,  that  we 
can  only  learn  by  practice  and  experience. 

Moreover,  what  has  been  said  holds  good  not  only  for 
the  qualitative  differences  of  sensations,  but  also,  in  any 
case,  for  the  greatest  and  most  important  part,  if  not  the 
whole,  of  our  various  perceptions  of  extension  in  space. 
In  their  bearings  on  this  question  the  new  doctrine  of 
binocular  vision  and  the  invention  of  the  stereoscope 
liave  been  of  importance.  All  that  the  sensation  of  the 
two  eyes  could  convey  to  us  directly,  and  without 
psychical  aid  was,  at  the  most,  two  somewhat  different 
flat  pictures  of  two  dimensions  as  they  lay  on  the  two 
retinae ;  instead  of  this  we  perceive  a  representation 
with  three  dimensions  of  the  thino's  around  us.  We 
are  sensible  as  well  of  the  distance  of  objects  not 
too  far  removed  from  us  as  of  their  perspective  juxta- 
position, and  compare  the  actual  magnitude  of  two 
objects  of  apparently  unequal  size  at  different  distances 
from  us  with  greater  certainty  than  the  apparent  equal 
magnitudes  of  a  finger,  say,  and  the  moon. 

One  explanation  only  of  our  perception  of  extension 
in  space,  which  stands  the  test  of  each  separate  fact,  can 
in  my  judgment  be  brought  forward  by  our  assuming 
with  Lotze  that  to  tlie  sensations  of  nerve-fibres,  dif- 
ferently situated  in  space,  certain  differences,  local  signs, 
attach  themselves,  the  significations  of  which,  as  regards 
space,  we  have  to  learn.  That  a  knowledge  of  their 
signification  may  be  attained  by  these  hypotheses,  and 
^^ith  the  help  of  the  movements  of  our  body,  and  that 
we  can  at  the  same  time  learn  which  are  the  right  move- 
ments to  bring  about  a  desired  result,  and  become 
conscious  of  having  arrived  at  it,  has  in  many  ways  been 
established. 

That  experience  exercised  an  enormous  influence  over 


ATM   AND   PROGRESS   OF   PHYSICAL   SCIENCE.     393 

tlie  signification  of  visual  pictures,  and,  in  cases  of  doubt, 
is  generally  the  final  arbiter,  is  allowed  even  by  those 
physiologists  who  wish  to  save  as  much  as  possible  of  the 
innate  harmony  of  the  senses  with  the  external  world. 
The  controversy  is  at  present  almost  entirely  confined  to 
the  question  of  the  proportion  at  birth  of  the  innate 
impulses  that  can  facilitate  training  in  the  understanding 
of  sensations.  The  assumption  of  the  existence  of  im- 
pulses of  this  kind  is  unnecessary,  and  renders  difficult 
instead  of  elucidating  an  interpretation  of  well-observed 
phenomena  in  adults.* 

It  follows,  then,  that  this  subtile  and  most  admirable 
harmony  existing  between  our  sensations  and  the  objects 
causing  them  is  substantially,  and  with  but  few  doubtful 
exceptions,  a  conformity  individually  acquired,  a  result 
of  experience,  of  training,  the  recollection  of  former  acts 
of  a  similar  kind. 

This  completes  the  circle  of  our  observations,  and  lands 
us  at  the  spot  whence  we  set  out.  We  found  at  the 
beginning,  that  what  physical  science  strives  after  is 
the  knowledge  of  laws,  in  other  words,  the  knowledge  how 
at  different  times  under  the  same  conditions  the  same 
results  are  brought  about ;  and  we  found  in  the  last 
instance  how  all  laws  can  be  reduced  to  laws  of  motion. 
We  now  find,  in  conclusion,  that  our  sensations  are  merely 
signs  of  changes  taking  place  in  the  external  world,  and 
can  only  be  regarded  as  pictures  in  that  they  represent 
succession  in  time.  P'or  this  very  reason  they  are  in  a 
position  to  show  directly  the  conformity  to  law,  in  regard 
to  succession  in  time,  of  natural  phenomena.  If,  under 
the  same  natural  circumstances,  the  same  action  take 
place,  a  person  observing  it  under  the  same  conditions 
will  find  the  same  series   of  impressions  regularly  recur. 

'  A  further  exposition  of  these  conditions  will  be  found  in  the  lectures  on 
the  Recent  Progress  of  the  Theory  of  Vision,  pp.  197  et  seq. 


394     ALM  Am)   PROGRESS   OF   PHYSICAL   SCIEXCE. 

That  which  our  organs  of  sense  perform  is  clearly  suffi- 
cient to  meet  the  demands  of  science  as  well  as  the  practical 
ends  of  the  man  of  business  who  must  rely  for  support  on 
the  knowledge  of  natural  laws,  acquired,  partly  involun- 
tarily by  daily  experience,  and  partly  purposely  by  the 
study  of  science. 

Having  now  completed  our  survey,  we  may,  perhaps, 
strike  a  not  unsatisfactory  balance.  Physical  science  has 
made  active  progress,  not  only  in  this  or  that  direction, 
but  as  a  vast  whole,  and  what  has  been  accomplished 
may  warrant  the  attainment  of  further  progress.  Doubts 
respecting  the  entire  conformity  to  law  of  nature  are 
more  and  more  dispelled  ;  laws  more  general  and  more 
comprehensive  have  revealed  themselves.  That  the  di- 
rection which  scientific  study  has  taken  is  a  healthy  one 
its  great  practical  issues  have  clearly  demonstrated  ;  and 
I  may  here  be  permitted  to  direct  particular  attention 
to  the  branch  of  science  more  especially  my  own.  In 
physiology  particularly  scientific  work  had  been  crippled 
by  doubts  respecting  the  necessary  conformity  to  law, 
which  means,  as  we  have  shown,  the  intelligibility  of 
vital  phenomena,  and  this  naturally  extended  itself  to 
the  practical  science  directly  dependent  on  physiology, 
namely,  medicine.  Both  have  received  an  impetus,  such 
as  had  not  been  felt  for  thousands  of  years,  from  the  time 
that  they  seriously  adopted  the  method  of  physical  science, 
the  exact  ob-ervation  of  phenomena  and  experiment.  As 
a  practising  physician,  in  my  earlier  days,  I  can  per- 
sonally bear  testimony  to  this.  I  was  educated  at  a 
period  when  medicine  was  in  a  transitional  stage,  when 
the  minds  of  the  most  thoughtful  and  exact  were  filled 
with  despair.  It  was  not  difficult  to  recognise  that  the 
old  predominant  theorising  methods  of  practising  medicine 
were  altogether  untenable ;  with  these  theories,  however, 
the  facts  on  which  they  had  actually  been  founded  had 


AIM   .'^D   PROGRESS   OF   PHYSICAL   SCIENCE.      395 

become  so  inextricably  entangled  that  they  also  were 
mostly  thrown  overboard.  How  a  science  should  be  built 
wp  anew  had  already  been  seen  in  the  case  of  the  other 
sciences  ;  but  the  new  task  assumed  colossal  proportions  ; 
few  steps  had  been  taken  towards  accomplishing  it, 
and  these  first  efforts  were  in  some  measure  but  crude 
and  clumsy.  We  need  feel  no  astonishment  that  many 
sincere  and  earnest  men  should  at  that  time  have 
abandoned  medicine  as  unsatisfactory,  or  on  principle 
given  themselves  over  to  an  exaggerated  empiricism. 

But  well  directed  efforts  produced  the  right  result 
more  quickly  even  than  many  had  hoped  for.  The 
application  of  the  mechanical  ideas  to  the  doctrine  of 
circulation  and  respiration,  the  better  interpretation  of 
thermal  phenomena,  the  more  refined  physiological  study 
of  the  nerves,  soon  led  to  practical  results  of  the  greatest 
importance ;  microscopic  examination  of  parasitic  struc- 
tures, the  stupendous  development  of  pathological  anatomy, 
irresistibly  led  from  nebulous  theories  to  reality.  We 
found  that  we  now  possessed  a  much  clearer  means  of 
distinguishing,  and  a  clearer  insight  into  the  mechanism 
of  the  process  of  disease  than  the  beats  of  the  pulse,  the 
urinary  deposit,  or  the  fever  type  of  older  medical  science 
had  ever  given  us.  If  I  might  name  one  department 
of  medicine  in  which  the  influence  of  the  scientific 
method  has  been,  perhaps,  most  brilliantly  displayed,  it 
would  be  in  ophthalmic  medicine.  The  peculiar  con- 
stitution of  the  eye  enables  us  to  apply  physical  modes  of 
investigation  as  well  in  functional  as  in  anatomical 
derangements  of  the  living  organ.  Simple  physical  ex- 
pedients, spectacles,  sometimes  spherical,  sometimes  cylin- 
drical or  prismatic,  suffice,  in  many  cases,  to  cure  dis- 
orders which  in  earlier  times  left  the  organ  in  a  condition 
of  chronic  incapacity;  a  great  number  of  changes  on 
the  other  hand,  which  formerly  did  not  attract  notice 
18 


396     AIM   AND    PROGRESS   OF   PHYSICAL   SCIENCE. 

till  they  induced  incurable  blindness,  can  now  be 
detected  and  remedied  at  the  outset.  From  the  very 
reason  of  its  presenting  the  most  favourable  ground  for 
the  application  of  the  scientific  method,  ophthalmology 
has  proved  attractive  to  a  peculiarly  large  number  of 
excellent  investigators,  and  rapidly  attained  its  present 
position,  in  which  it  sets  an  example  to  the  other  depart- 
ments of  medicine,  of  the  actual  capabilities  of  the 
true  method,  as  brilliant  as  that  which  astronomy  for 
long  had  offered  to  the  other  branches  of  physical  science. 

Though  in  the  investigation  of  inorganic  nature  the 
several  European  nations  showed  a  nearly  uniform  ad- 
vancement, the  recent  progress  of  physiology  and  medi- 
cine is  pre-eminently  due  to  Grermany.  I  have  already 
spoken  of  the  obstacles  which  formerly  delayed  progress  in 
this  direction.  Questions  respecting  the  nature  of  life  are 
closely  bound  up  with  psychological  and  ethical  inquiries. 
It  demands,  moreover,  that  we  bestow  on  it  unwearied 
diligence  for  purely  ideal  purposes,  without  any  approach- 
ing prospect  of  the  pure  science  becoming  of  practical 
value.  And  we  may  make  it  our  boast  that  this  exalted 
and  self-denying  assiduity,  this  labour  for  inward  satis- 
faction, not  for  external  success,  has  at  all  times  peculiarly 
distinguished  the  scientific  men  of  Germany. 

AA'hat  has,  after  all,  determined  the  state  of  things 
in  the  present  instance  is  in  my  opinion  another  cir- 
cumstance, namely,  that  we  are  more  fearless  than  others 
of  the  consequences  of  the  entire  and  perfect  truth. 
Both  in  England  and  France  we  find  excellent  inves- 
tigators who  are  capable  of  working  with  thorough 
energy  in  the  proper  sense  of  the  scientific  methods ; 
hitherto,  however,  they  have  almost  always  had  to  bend 
to  social  or  ecclesiastical  prejudices,  and  could  only  openly 
express  their  convictions  at  the  expense  of  their  social 
influence  and  their  usefulness. 


AIM   AND    PROGRESS    OF   PHYSICAL    SCIENCE.      397 

Grermany  has  advanced  with  bolder  step  :  she  has  had 
the  full  confidence,  which  has  never  been  shaken,  that 
truth  fully  known  brings  with  it  its  own  remedy  for 
the  danger  and  disadvantage  that  may  here  and  there 
attend  a  limited  recognition  of  what  is  true.  A  labour- 
loving,  frugal,  and  moral  people  may  exercise  such  bold- 
ness, may  stand  face  to  face  with  truth  ;  it  has  nothing 
to  fear  though  hasty  or  partial  theories  be  advocated, 
even  if  they  should  appear  to  trench  upon  the  founda- 
tions of  morality  and  society. 

We  have  met  here  on  the  southern  frontier  of  our 
country.  In  science,  however,  we  recognise  no  political 
boundaries,  for  our  country  reaches  as  far  as  the  German 
tongue  is  heard,  wherever  German  industry  and  German 
intrepidity  in  striving  after  truth  find  favour.  And 
that  it  finds  favour  here  is  shown  by  our  hospitable 
reception,  and  the  inspiriting  words  with  which  we  have 
been  greeted.  A  new  medical  faculty  has  been  established 
here.  We  will  wish  it  in  its  career  rapid  progress  in  the 
cardinal  virtues  of  German  science,  for  then  it  will  not 
only  find  remedies  for  bodily  suffering,  but  become  an 
active  centre  to  strengthen  intellectual  independence, 
steadfastness  to  conviction  and  love  of  truth,  and  at  the 
same  time  be  the  means  of  deepening  the  sense  of  unity 
throughout  our  country. 


THE    WORKS    OF 

Prof.  JOHN  TYNDALL,  LLD.,  F.H.S. 


I. 
HEAT   AS   A   MODE   OF   MOTION. 

Cue  vol.,  i2mo.     Cloth,  $2.00. 

"  My  aim  has  been  to  rise  to  the  level  of  these  questions  from  a  basis  so  elementary  that 
a  person  possessing  any  imaginative  faculty  and  powta:  of  concentration  might  accoio* 
p-iny  me." — From  Aitthor's  Prkfack. 

II. 

ON   SOUND. 

A  Course  of  Eight  Lectures  delivered  at  the  Royal  Institution  of  Great 
Britain.     One  vol.     With  Illustrations.     l2mo.     Cloth,  $2.00. 
*'  In  the  following  pages  I  have  tried  to  render  the  science  of  Acoustics  interesting  to 
all  intelligent  persons,  including  those  who  do  not  possess  any  special  scientific  culture." 
From  Author's  Preface. 

IIL 

FRAGMENTS  OF  SCIENCE   FOR   UNSCIENTIFIC 
PEOPLE. 

A  Series  of  Detached  Essays,  Lectures,  and  Reviews.    One  vol.,  i2rao. 
Cloth,  $2.00. 

"  My  motive  in  writing  these  papers  was  a  desire  to  extend  sympathy  for  science  be- 
yond the  limits  of  the  scientific  public.  .  .  .  From  America  the  impulse  came  which  in. 
duced  me  to  gather  these  '  Fragments,'  and  to  my  friends  in  the  United  Sutes  I  dedicate 
them." — From  Author's  Prefacb. 

IV. 
LIGHT  AND   ELECTRICITY. 

Notes  of  Two  Courses  of  Lectures  before  the  Royal  Institution  of  Great 
Britain.     One  vol.,  l2mo.     Cloth,  $1.25. 

"  In  thus  clearly  and  sharply  stating  the  fundamental  principles  of  Electrical  and  Op- 
tical Science,  Prof.  Tyndall  has  earned  the  cordial  thanks  of  all  interested  in  education."— 
From  American  Editor's  Preface. 

D.  APPLETON  &  CO.,  Publishers, 

549  &  561   Broadway,  N.  Y. 


THE    WORKS    OF 

Prof.  JOHN  TYNDALL,  LLD.,  F.R.S. 


V. 
HOURS  OF   EXERCISE   IN   THE   ALPS. 

One  vol.,  i2mo.     With  Illustrations.     Cloth,  $2.00. 

"  The  present  volume  is  for  the  most  part  a  record  of  bodily  action,  written  partly  to 
preserve  to  myself  the  memory  of  strong  and  joyous  hours,  and  partly  for  the  pleasure  of 
those  who  find  exhilaration  in  descriptions  associated  with  mountain-life."— From  Author's 
Preface. 

VI. 

FARADAY    AS    A    DISCOVERER. 

One  vol.,  l2mo.     Cloth,  $1.00. 

*'It  has  been  thought  desirable  to  give  you  and  the  world  some  image  of  Michael 

Faraday  as  a  scientific  investigator  and  discoverer I  have 

returned  from  my  task  with  such  results  as  I  could  gather,  and  also  with  the  wish  that 
these  results  were  more  worthy  than  they  are  of  the  greatness  of  my  theme." — The 
Author. 

VII. 

FORMSOF  WATER,  IN  CLOUDS,  RAIN,  RIVERS,  ICE, 
AND  GLACIERS. 

This  is  the  first  volume  of  the  International  Scientific  Series,  and  is  a  valu- 
able and  interesting  work.     One  vol.,  I2mo,     Cloth,  $1.50. 

VIII. 

CONTRIBUTIONS  TO   MOLECULAR   PHYSICS   IN   THE 
DOMAIN   OF   RADIANT   HEAT. 

A  Series  of  Memoirs  published  in  the  *•  Philosophical  Transactions  "  and 
*'  Philosophical  Magazine."     With  Additions. 

D.  APPLETON  &  CO.,  Publishers, 

649  &  551  Broadway,  N.  Y. 


DESCHANEL'S    NATURAL    PHILOSOPHY. 


Natural  Philosophy: 

AN  ELEMENTARY  TREATISE. 
By   PROFESSOR    DESCHANEL,   of  Paris. 

Translated,  with  Extensive  Additions, 
By  J.  D.  Everett,  D.  C.  L.,  F.  R.  S., 

PBOFESSOB  OF  NATURAL  PniLOSOPHY  IN  THE  QITEEN'S  COLLEGE,  BELFAST. 

1  vol.,  medium  8vo.     Illustrated  by  760  "Wood  Engravings  and  3  Colored  Plates. 
Cloth,  $    .    Published,  also,  separately,  in  Four  Parts.    Limp  cloth,  each  $1.75. 

Part  I.  MECHANICS,  HYDROSTATICS,  and  PNEUMATICS.    Part  II.  HEAT. 
Part  III.  ELECTRICITY  and  MAGNETISM.    Part  IV.  SOUND  and  LIGHT. 

Saturday  Review. 

"  Systematically  arranged,  clearly  written,  and  admirably  illustrated,  showing  no 
less  than  than  760  engravings  on  wood  and  three  colored  plates,  it  forms  a  model  work 
for  a  class  of  experimental  physics.  Far  ftom  losing  in  its  English  dress  any  of  the 
qualities  of  matter  or  style  which  distinguished  it  in  its  original  form,  it  may  be  said 
to  have  gained  in  the  able  hands  of  Professor  Everett,  both  by  way  of  arrangement 
and  of  incorporation  of  fresh  matter,  without  parting  in  the  translation  with  any  of  the 
freshness  or  force  of  the  author^s  text*' 

AtliencBum. 
♦'  A  good  working  class-book  for  students  in  experimental  physics." 

Westminster  Review. 

"An  excellent  handbook  of  physics,  especially  suitable  for  self-instruction.  .  .  . 
The  work  is  published  in  a  magnificent  style ;  the  woodcuts  especially  are  admirable." 

Quarterly  Journal  of  Science. 

♦'  We  have  no  work  in  our  own  scientific  Uterature  to  be  compared  with  it,  and  we 
are  glad  that  the  translation  has  fallen  into  such  good  hands  as  those  of  Professor 
Everett.  ...  It  will  form  an  admirable  text-book." 

Nature. 

"  The  engravings  with  which  the  work  is  illustrated  are  especially  good,  a  point  in 
which  most  of  our  English  scientific  works  are  lamentably  deficient.  The  clearness 
of  Deschaners  explanations  is  admirably  preserved  in  the  translation,  while  the  value 
of  the  treatise  is  considerably  enhanced  by  some  important  additions.  .  .  .  We  believe 
the  book  will  be  found  to  supply  a  real  need." 

D.  APPLETON   &  CO.,  New  York. 


New   Scientific  W^orks. 


The  Beginnings  of  Life; 

Being  some  Account  of  the  Nature,  Modes  of  Origin  and  Transformation 
of  the  Lower  Organisms.  By  H.  Charlton  Bastian,  M.  D.,  F.  R.  S. 
2  vols.,  8vo.     With  upward  of  loo  Illustrations.     Price,  $5.00. 

"His  preliminary  chapters  on  the  correlation  of  the  vital  and  physical  forces,  on  the 
nature  and  theories  of  life,  on  organized  and  organizable  matter,  on  the  relations  of  the  ani- 
mal, vegetable,  and  mineral  kingdoms,  and  on  cell-phenomena  and  cell-doctrines,  form  the 
clearest  and  most  readable  exposition  of  these  subjects  that  we  have  yet  seen,  and  they  have 
a  value  quite  independent  of  the  special  inquiry  to  which  they  are  an  introduction." — Fop- 
ular  Science  Monthly. 

"  It  is  a  book  which  will  make  its  mark,  and  must  produce  a  powerful  sensation."— 
Nature. 

The  Ancient  Stone  Implements,  Weapons,  and 
Ornaments  of  Great  Britain. 

By  John  Evans,  F.  R.  S.,  F.  S.  A.,  Honorary  Secretary  of  the  Geological 

and   Numismatic   Societies   of  London,    eta      i    vol.,  8vo.     With  2 

Plates  and  476  Woodcuts.     Price,  $5.00. 

"We  congratulate  all  those  who  are  interested  in  these  researches — and  they  are  now 
many — on  the  ample  and  valuable  additions  which  the  author  has  made  to  this  new  and  in- 
teresting chapter  in  the  history  of  our  race." — Nature. 

Town  Geology. 

By  the  Rev.  Chas.  Kingsley,  F.  L.  S.,  F.  G.  S.,  Canon  of  Chester,  i 
vol.     Cloth.     Price,  $1.50. 

An  interesting  and  valuable  book.  The  high  standing  of  the  author  is  a  sufficient  guar- 
anty for  the  excellence  of  the  work,  and  will  secure  for  it  an  extensive  circulation. 


A  Hand-Book  of  Chemical  Technology. 

By  Rudolf  Wagner,  Ph.  D.,  Professor  of  Chemical  Technology  at  the 
University  of  Wurtzburg.  Translated  and  edited,  from  the  eighth 
German  edition,  with  extensive  Additions.  By  Wm.  Crookes,  F.  R.  S. 
With  336  Illustrations,     i  vol.,  8vo.     761  pages.     Cloth,  $5.00. 

The  several  editions  of  Professor  Rudolf  Wagner's  "  Handbuch  der  Chemischen  Tech- 
nologic "  have  succeeded  each  other  so  rapidly,  that  no  apology  is  needed  in  offering  a 
l^nslation  to  the  public. 


D.  APPLETON  &  CO.,  Publishers, 

549   <2r»  551  Broadway y  New   York. 


Tht  Colored  Plates  illustrating  this  edition  of  the  work,  requiring  great  car* 
in  pHnting,  were  executed  in  London. 


SPECTRUM    ANALYSIS, 

In  its  Application  to  Terrestrial  Substances,  and  the  Physical 
Constitution  of  the  Heavenly  Bodies, 

Familiarly  explained,  by  Dr.  H.  Schellen,  Director  der  Realschule 
I.  0.  Cologne.  Translated  from  the  second  enlarged  and  revised 
German  edition,  by  Jane  and  Caroline  Lassell.  Edited,  with 
Notes,  by  William  Huggins,  LL.  D.  With  numerous  Woodcuts, 
Colored  Plates,  and  Portraits ;  also,  Angstrom's  and  Kirchhoff 's 
Maps.     455  pages,  8vo,  cloth.     Price,  $6.00. 


From  the  CJiemical  News. 

"This  admirable  work  does  credit  to,  or  should  we  say  is  worthy  of  the 
author,  the  translators,  and  the  editor.  The  first  part  treats  on  the  artificial 
sources  of  high  degrees  of  heat  and  light ;  the  second  on  Spectrum  Analysis 
in  its  application  to  the  heavenly  bodies.  We  must  approve  the  method  fol- 
lowed in  the  translation,  and  by  the  editor.  In  many  translations  the  views 
of  the  author  are  suppressed,  in  order  that  the  views  of  the  translator  or 
editor  may  be  expounded;  but  here  Dr.  Hoggins,  however  leniently  such  a 
fault  might  have  been  looked  upon  with  him,  has  permitted  the  author's 
views  to  remain  intact,  clearly  stating  his  own  and  wherein  Ues  the  differ- 
ence." 

From  tJie  Chicago  Post. 

"  The  object  of  this  volnme  is  to  introduce  the  general  reader  into  a  new 
realm  of  science,  and  acquaint  him  with  the  particulars  and  tlie  results  of 
the  most  brilliant  discovery  of  the  present  century.  Whoever  has  an  appre- 
ciative sense  of  the  beauties  and  wonders  of  Nature,  illuminated  by  science, 
will  find  this  volume  a  rich  mine  of  enjoyment  which  he  will  do  wisely  to 
explore." 

From,  the  Philadelphia  Age. 

"  The  contents  are  formidable  in  appearance,  but  the  average  reader  will 
find  its  exposition  easily  intelligible.  To  many  the  revelations  of  this  book, 
80  marvellously  minute,  and  vet  so  unerringly  accurate,  will  be  as  wonder- 
ful as  the  stories  of  the  '  Arabian  Nights.' " 

From  the  Boston  Globe. 

"  Certainly,  as  regards  mere  knowledge,  the  Spectrttm  Anai,tsis  has  let 
us  into  many  secrets  of  the  physical  universe,  which  Newton  and  La  Place 
would  have  declared  impossible  for  man's  intellect  to  attain.  The  science 
is  still  in  its  infancy,  but  it  is  prosecuted  by  some  of  the  ablest,  most  pa- 
tient, and  most  enthusiastic  observers,  and  some  of  the  keenest  thinkers, 
at  present  existing  on  our  little,  insignificant  physical  globe." 

D.  APPLETON  &  CO.,  Publishers, 

549  &  551  BROADWAY,  N.  T. 


A  New  Magazine  for  Students  and  Cultivated  Eeaders. 


THE 


POPULAR  SCIENCE  MONTHLY, 


CONDUCTED    BY 
Professor  E.   L.  VOUMANS. 


The  Rowing  importance  of  scientific  knowledge  to  all  classes  of  the 
community  calls  for  more  efficient  means  of  diffusing  it.  The  Popular 
Science  Monthly  has  been  started  to  promote  this  object,  and  supplies  a 
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It  contains  instructive  and  attractive  articles,  and  abstract?  of  articles, 
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tions of  domestic  life. 

It  is  designed  to  give  especial  prominence  to  those  branches  of  science 
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of  society  and  government.  How  the  various  subjects  of  current  opinion 
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In  its  literary  character,  this  periodical  aims  to  be  popular,  without  be- 
ing superficial,  and  appeals  to  the  intelligent  reading-classes  of  the  commu- 
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subjects,  and  who  will  address  the  non-scientific  public  for  purposes  of  ex- 
position and  explanation. 

It  will  have  contributions  from  Herbert  Spencer,  Professor  Huxley, 
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country." — Home  journal. 

'•  The  initial  number  is  admirably  constituted." — Evening  Mail. 

"In  our  opinion,  the  right  idea  has  been  happily  hit  in  the  plan  of  this  new  monthly." 
•^Btiffalo  Courier. 

*'  A  journal  which  promises  to  be  of  eminent  value  to  the  cause  of  popular  education  in 
this  country." — N.  Y.  Tribune. 

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5^p^  Payment^  in  all  cases,  must  be  in  advance. 

Remittances  should  be  made  by  postal  money-order  or  check  to  the  Publishers, 

r.  APPLETON  &  CO.,  549  &  551  Broadway,  New  York. 


NEW  WORK   BY  MR.  DARWIN. 


Now  ready,     i  vol.     Thick  i2mo.     With  Illustrations.     $3.50. 

The  Expression  of  the  Emotions 
in  Man  and  Animals. 

By  CHARLES  DARWIN,  F.  R.  S.,  Author  of  the  "  Origin  of  Species,"  etc.,  etc. 

"Whatever  one  thinks  of  Mr.  Darwin's  theory,  it  must  be  admitted  that  his  great 
powers  of  observation  are  as  conspicuous  as  ever  in  this  inquiry.  During  a  space  ot 
more  than  thirty  years,  he  has,  with  exemplary  patience,  been  accumulating  informa- 
tion from  all  available  sources.  The  result  of  all  this  is  undoubtedly  the  collection  of  a 
mass  of  minute  and  trustworthy  information  which  must  possess  the  highest  value, 
whatever  may  be  the  conclusions  ultimately  deduced  from  it." — London  Times. 

"  It  is  almost  needless  to  say  that  Mr.  Darwin  has  brought  to  this  work  vast  stores 
of  erudition,  accumulated  treasures  of  careful  observation,  and  all  the  devices  of  an 
acute  and  fertile  ingenuity;  for  these  are  qualities  which  are  conspicuous  in  all  he 
writes.  But  it  may  be  as  well  to  add  that  the  book  is  verj-  attractive  even  to  general 
readers.  It  is  comparatively  light  and  easy  reading,  full  of  amusing  anecdote  ;  and  the 
illustrations,  whether  due  to  the  sun's  rays  or  to  the  engraver's  point,  are  excellent." — 
Guardian. 

"  Those  of  our  readers  who  know  the  charm  of  Darwin's  former  works,  how  he 
leads  his  readers  on  to  his  conclusions  in  the  clearest  and  most  attractive  English,  will 
experience  more  than  their  usual  treat  when  they  sit  down  to  this  book.  Never  was 
more  truly  realized  the  saying  about  men  laboring  and  others  entering  into  the  fruit  of 
their  labors.  The  illustrations  are  excellent,  and  recourse  has  been  had  to  photographs 
in  rendering  the  more  telling  of  the  physiognomical  expressions.  Even  the  most  an- 
tagonistic of  anti-Darwinians  will  not  hesitate  to  admit  how  much  he  has  learned  from 
a  careful  study  of  the  work  before  us." — Science  Gossip. 


RECENTLY   PUBLISHED. 


A  NEW  EDITION  OF 


Darwin's  Origin  of  Species. 

FROM  THE  SIXTH  AND  LAST  ENGLISH  EDITION, 
Containing  the  Author'' s  Latest  Corrections  and  Additions, 

From  an  entirely  new  set  of  stereotype  plates.     i2mo.     Cloth.     Price,  $2.00. 

D.  APPLETON  &  CO.,  PubUshers. 


An  Important  Work  for  Manufacturers,  Chemists,  and  Students. 


A    HAND-BOOK 


Chemical  Technology. 

By  Rudolph  Wagner,  Ph.  D., 

PROFESSOR  OF   CHEMICAL  TECHNOLOGY  AT  THE   UNIVERSITY   OF  WURTZBURG. 

Translated  and  edited,  from  the  eighth  German  edition,  with  extensive 
Additions, 

By  Wm.  Crookes,  F.  R.  S. 

With -^-^^  Illustrations.     ivol.,2,vo.     "jti  pages.     CZotA,  $5.00. 


The  several  editions  of  Professor  Rudolph   Wagner's  *'  Handbuch  der 

Chemise  hen    Technologies^    have  succeeded  each  other  so 

rapidly,  that  no  apology  is  needed  in  offering 

a    translation    to   the  public. 

Under  the  head  of  Metallurgic  Chemistry,  the  latest  methods  of  preparing  Iron, 
Cobalt,  Nickel,  Copper,  Copper  Salts,  Lead  and  Tin  and  their  Salts,  Bismuth,  Zinc, 
Zinc  Salts,  Cadmium,  Antimony,  Arsenic,  Mercury,  Platinum,  Silver,  Gold,  Man- 
ganates,  Aluminum,  and  Magnesium,  are  described.  The  various  applicat'ons  of  the 
Voltaic  Current  to  Electro-Metallurgy  follow  under  this  division.  The  Preparation  of 
Potash  and  Soda  Salts,  the  Manufacture  of  Sulphuric  Acid,  and  the  Recovery  of  Sul- 
phur from  Soda- Waste,  of  course  occupy  prominent  places  in  the  consideration  of 
chemical  manufactures.  It  is  difficult  to  over-estimate  the  mercantile  value  of  Mond's 
process,  as  well  as  the  many  new  and  important  applications  of  Bisulphide  of  Carbon. 
The  manufacture  of  Soap  will  be  found  to  include  much  detail.  The  Technology  of 
Glass,  Stoneware,  Limes  and  Mortars,  will  present  much  of  interest  to  the  Builder  and 
Engineer.  The  Technology  of  Vegetable  Fibres  has  been  considered  to  include  the 
preparation  of  Flax,  Hemp,  Cotton,  as  well  as  Paper-making;  while  the  applications 
of  Vegetable  Products  will  be  found  to  include  Sugar-boiling,  Wine  and  Beer  Brewing, 
the  Distillation  of  Spirits,  the  Baking  of  Bread,  the  Preparation  of  Vinegar,  the  Preser- 
vation  of  Wood,  etc. 

Dr.  Wagner  gives  much  information  in  reference  to  the  production  of  Potash  from 
Sugar-residues.  The  use  of  Baryta  Salts  is  also  fully  described,  as  well  as  the  prepa- 
ration of  Sugar  from  Beetroots.  Tanning,  the  Preservation  of  Meat,  Milk,  etc.,  the 
Preparation  of  Phosphorus  and  Animal  Charcoal,  are  considered  as  belonging  to  the 
Technology  of  Animal  Products.  The  Preparation  of  the  Materials  for  Dyeing  has 
necessarily  required  much  space  ;  while  the  final  sections  of  the  book  have  been  de- 
voted to  the  Technology  of  Heating  and  Illumination. 

D.  APPLETON   &   CO.,  Publishers. 


f'*-^.. 


